age problems

The sum of Josh's age plus his cousin Simon's age is 53. Simon was twice as old as Josh when Josh was 7. How old is Simon now? 37 30 46 23

When Josh was 7, Simon was twice as old as him so was 7 x 2 = 14 years old. This tells us that Josh is 7 years younger than Simon, which can be written J = S - 7 where S represents Simon's age and J represents Josh's age. The sum of Josh's current age and Simon's current age is 53, so: S + J = 53 Substitute S - 7 for J into the equation above so that there is only one variable: S + (S - 7) = 53 Combine like terms 2S - 7 = 53 Add 7 to each side 2S = 60 Divide both sides by 2 S = 30 So Simon is 30 years old.

Henry is 11 years old and Nick is 26 years old. How many years ago was Nick 4 times as old as Henry? 6 3 4 9

x number of years ago, both Nick and Henry were x years younger, so Nick's age was 26 - x And Henry's age was 11 - x Nick was four times as old as Henry x years ago, which can be written as: 26 - x = 4(11 - x) Distribute 26 - x = 44 - 4x Add 4x to both sides 26 + 3x = 44 Subtract 26 from both sides 3x = 18 Divide both sides by 3 x = 6 so six years ago (when Henry was 5 and Nick was 20) Nick was four times older than Henry.

Andy is 5 years older than his sister. 12 years ago the sum of their ages was 71, how old is Andy? 60 45 55 50

Andy is five years older than his sister so Andy's age can be written A = s + 5 where A represents Andy's current age and s represents Andy's sister's current age. Rearranging this expression and solving for s gives A - 5 = s. 12 years ago, Andy and his sister were 12 years younger so: Andy's age was A - 12 Andy's sister's age was s - 12 12 years ago the sum of their ages was 71 so: (A - 12) + (s - 12) = 71 Now, substitute A - 5 for s into the equation so that there is only one variable: (A - 12) + ((A - 5) - 12) = 71 Combine like terms 2A - 29 = 71 Add 29 to both sides 2A = 100 Divide both sides by 2 A = 50 So Andy is 50 years old.

Ben is one-fifth the age of Jude. If Jude is fifteen, how many years will pass before Ben is one-third of Jude's age? 3 6 15 1

Ben is one-fifth the age of Jude so is (1/5)15 = 3 years old. In x number of years, Jude's age will be J + x and Ben's age will be B + x. Jude's age will be three times Ben's age, which can be written: J + x = 3(B + x) We can substitute Ben and Jude's ages into the equation since we know that Ben is 3 years old and Jude is 15 years old, so J = 15 and B = 3: J + x = 3(B + x) (15) + x = 3((3) + x) 15 + x = 9 + 3x Now solve the equation to find x: 15 + x = 9 + 3x Subtact 9 from both sides 6 + x = 3x Subtract x from both sides 6 = 2x Divide both sides by 2 3 = x So the number of years that need to pass before Ben is one-third of Jude's age is 3.

Charles is 9 years older than Andrea. The sum of their ages in 7 years time will be 65. What is Andrea's age now? 25 24 30 21

Charles is 9 years older than Andrea which can be written as C = A + 9, where C represents Charles's age and A represents Andrea's age. In 7 years time both Charles and Andrea will be 7 years older so: Charles's age = C + 7 Andrea's age = A + 7 ...and the sum of their ages will be 65: (C + 7) + (A + 7) = 65 Now, substitute C = A + 9 into the equation so that there is only one variable: ((A + 9) + 7) + (A + 7) = 65 Solve the equation for A: A + 16 + A + 7 = 65 2A + 23 = 65 Subtract 23 from both sides 2A = 42 Divide both sides by 2 A = 21 so Andrea's age is 21.

David is now three times as old as James, but in two years time he will be twice as old as James. How old is David now? 8 1 6 2

David is now three times as old as James, which can be written D = 3J, where D is David's current age and 'J' is James's current age. In two years, both David and James will be two years older, so: David's age will be D + 2, James's age will be J + 2. In two years, David's age will be twice that of James's age, so D + 2 = 2(J + 2) Substituting D = 3J into the equation so that we only have one variable, the equation can be written: 3J + 2 = 2(J + 2) Now solve the equation for J, 3J + 2 = 2J + 4 Subtract 2J from both sides J + 2 = 4 Subtract 2 from both sides J = 2 so James is now 2 years old, and David is three times David's age so 3 x 2 = 6 years old.

Eddie is 6 years older than his sister Rebecca. In 4 years time, he will be twice as old as Rebecca. What is the current sum of their ages? 9 14 10 8

Eddie is 6 years older than Rebecca which can be written as E = R + 6 where E represents Eddie's age and R represents Rebecca's age. In four years time both Eddie and Rebecca will be 4 years older: Eddie's age = E + 4 Rebecca's age = R + 4 ... and Eddie's age will be twice Rebecca's age: (E + 4) = 2(R + 4) Substitute E = R + 6 into the equation so that there is only one variable: ((R + 6) + 4) = 2(R + 4) Solve the equation for R: R + 10 = 2R + 8 Subtract 8 from both sides R + 2 = 2R Subtract R from both sides 2 = R So Rebecca is 2 and Eddie is 6 years older so is 2 + 6 = 8 years old. The sum of their ages is 8 + 2 = 10.

Sue was four times older than George 8 years ago. If Sue is now 56 then how old is George? 12 48 14 20

Eight years ago, Sue was 56 - 8 = 48 years old. Since Sue was four times older than George eight years ago, George was 48 ÷ 4 = 12 years old eight years ago. George is now 12 + 8 = 20 years old.

Luke is three times as old as Lauren. If Lauren will be 15 in four years time, how many years older than Lauren is Luke? 11 22 15 33

If Lauren will be fifteen in four years time, she is currently 15 - 4 = 11 years old. Luke is currently three times as old as Lauren so he is 11 x 3 = 33 years old. Luke is 33 - 11 = 22 years older than Lauren.

Three years ago, Marie was three times as old as Jenny. In three years time Marie will be twice as old as Jenny. How old is Marie now? 9 6 12 21

If M represents Marie's current age and J represents Jenny's current age, three years ago Marie and Jenny were both 3 years younger, so Marie's age was M - 3, and Jenny's age was J - 3. Marie was three times as old as Jenny so: M - 3 = 3(J - 3) In 3 years time Marie will be twice as old as Jenny: M + 3 = 2(J + 3) So we have 2 equations: M - 3 = 3(J - 3) M + 3 = 2(J + 3) We can solve this problem by the substitution method for simultaneous equations. Solve the first equation for Jenny's age: M - 3 = 3(J - 3) Distribute M - 3 = 3J - 9 Add 9 to both sides M + 6 = 3J Divide both sides by 3 1/3M + 2 = J Substitute J = 1/3M + 2 into the second equation so that we only have one variable: M + 3 = 2(J + 3) M + 3 = 2((1/3M + 2) + 3) Combine like terms M + 3 = 2(1/3M + 5) Distribute M + 3 = 2/3M + 10 Substract 2/3M from both sides 1/3M + 3 = 10 Substract 3 from both sides 1/3M = 7 Multiply both sides by 3 M = 21 so Marie is 21 years old.

If Tom was 2 years older, he would be three times as old as his sister Ella, who is 5. How old is Tom? 10 12 13 15

If Tom was three times as old as Ella he would be 3 x 5 = 15 years old. He is 2 years younger than this so he is 15 - 2 = 13 years old.

One-quarter of Ellen's age 5 years from now plus one-third of her age 5 years ago equals 34. How old is Ellen now? 65 60 59 70

If x represents Ellen's age now then "one-quarter of Ellen's age 5 years from now" = 1/4(x + 5) ...and "one-third of her age 5 years ago" = 1/3(x - 5) These two combined equals 34: 1/4(x + 5) + 1/3(x - 5) = 34 Now, we can solve this equation to find x: 1/4(x + 5) + 1/3(x - 5) = 34 Distribute 1/4x + 5/4 + 1/3x - 5/3 = 34 Get common denominators to combine like terms 3/12x + 4/12x + 15/12 - 20/12 = 34 Combine like terms 7/12x - 5/12 = 34 Multiply both sides by 12 7x - 5 = 408 Add 5 to both sides 7x = 413 Divide both sides by 7 x = 59 So Ellen is 59 years old

In 1 year, Robert will be 6 times as old as his grandson. The current total of their ages is 89. How old is Robert now? 82 78 72 77

In 1 year, both Robert and his grandson will be one year older so the total of their ages will be 89 + 2 = 91. Robert's age will be six times that of his grandson so can be represented as R = 6g, where 'g' equals the age of his grandson. The sum of their ages next year equals 91 so: 6g + g = 91 Now, solve the equation to find g: 7g = 91 Divide both sides by 7 g = 13 So Robert's grandson will be 13 years old next year, and Robert will be 6 x 13 = 78 years old. This year Robert is 78 - 1 = 77 years old.

Jason is now one-third the age of his uncle Paul. 7 years ago, Jason was 3 years older than one-quarter of his uncle's age. How old will Jason be in 7 years time? 30 40 43 18

Jason is now one-third the age of his uncle Paul, which means Jason's Uncle is now three times older than Jason, which can be written U = 3J, where U is Jason's Uncle's current age and 'J' is Jason's current age. Seven years ago, both Jason's Uncle and Jason were seven years younger, so: Jason's Uncle's age was U - 7, Jason's age was J - 7 Seven years ago, "Jason was 3 years older than one-quarter of his uncle's age" which can be written as: Jason's Uncle's age was 3 years less than four times Jason's age, so J - 7 = 1/4(U - 7) + 3 Now substitute U = 3J into the equation so that there is only one variable: J - 7 = 1/4(3J - 7) + 3 Distribute J - 7 = 3/4J - 7/4 + 3 Combine like terms and subtract 3/4J from both sides 1/4J - 7 = 5/4 Add 7 to both sides (same as adding 28/4) 1/4J = 33/4 Multiply both sides by 4 J = 33 So Jason is currently , and in 7 years will be 33 + 7 = 40 years old.

Jeremy is 18 years younger than Helen, and the sum of both their ages is 82. How old is Helen? 64 46 50 32

Jeremy is 18 years younger than Helen, so Jeremy's age is H - 18, where H represents Helen's age. Jeremy's age = H - 18 Helen's age = H The sum of their ages is 82, so H + (H - 18) = 82 Solve to find Helen's age: H + H - 18 = 82 2H - 18 = 82 Add 18 to both sides 2H = 100 Divide both sides by 2 H = 50

Lucy is now twice as old as her cousin Anne, but ten years ago she was three times as old as Anne, how old is Lucy now? 10 30 40 20

Lucy is now twice as old as Anne, which can be written L = 2A, where L is Lucy's current age and A is Anne's current age. Ten years ago, both Anne and Lucy were ten years younger, so : Lucy's age will be L - 10, and Anne's age will be A - 10. Ten years ago, Lucy's age was three times that of Anne's, so L - 10 = 3(A - 10) Substituting L = 2A into the equation so that we only have one variable, the equation can be written: 2A - 10 = 3(A - 10) Now solve to find A: 2A - 10 = 3A - 30 Subtract 2A from both sides -10 = A - 30 Add 30 to both sides 20 = A So Anne is now 20 years old, and Lucy is therefore 40 years old, twice Anne's age.

Neil is 5 years younger than Adam. If in 12 years time the sum of both their ages will be 59, what is the current ratio of Adam's age to Neil's age? 3:5 5:4 4:3 3:4

NOW Neil is 5 years younger than Adam so N = A - 5 where N is Neil's age now and A is Adam's age now. In 12 years time, both Adam and Neil will be 12 years older, so: In 12 Years Adam's age will be A + 12, Neil's age will be N = (A + 12) - 5. Their combined ages will equal 59, so we can find Adam's age now as follows: (A + 12) + ((A + 12) - 5) = 59 Solve for A: (A + 12) + (A + 12 - 5) = 59 2A + 19 = 59 Subtract 19 from both sides 2A = 40 Divide both sides by 2 A = 20. So Adam is 20 years old, and Neil is 5 years younger so is 20 - 5 = 15 years old. The ratio of Adam's age to Neil's age is 20:15, or 4:3.

Rachel is now 27 years older than her daughter, but in 8 years, Rachel will be 7 years younger than 3 times her daughter's age. How old is Rachel now? 33 27 36 34

Rachel is 27 years older than her daughter so her age can be written as R = d + 27 where R represents Rachel's current age and d represents her daughter's current age. In 8 years time Rachel's age will be R + 8 Substituting in R = d + 27 R = (d + 27) + 8 R = d + 35 and her daughter's age will be d + 8. Rachel's age in 8 years time (d + 35) is 7 years younger than three times her daughter's age which can be written as: (d + 35) = 3(d + 8) - 7 Now, solve the equation to find d: d + 35 = 3(d + 8) - 7 Distribute d + 35 = 3d + 24 - 7 Combine like terms d + 35 = 3d + 17 Subtract d from both sides 35 = 2d + 17 Subtract 17 from both sides 18 = 2d Divide both sides by 2 9 = d So Rachel's daughter is 9 years old, Rachel is 27 years older than her daughter so is 27 + 9 = 36 years old.

Lily is 2 years older than Louis, and the product of their ages is 24. How old is Lily? 8 6 4 2

The factors of 24 are 1,24; 2,12; 3,8; 4,6; 8,12, out of these factors, 4 and 6 are the only pair with a difference of two. Since Lily is 2 years older than Louis, Lily is 6 and Louis is 4. Another approach would be to define Lily's age as x and Louis' age as y. Since Lily is 2 years older than Louis we could express her age as x = y + 2 Rearranging and solving for Louis' age gives y = x - 2 We are also told that the products of their ages is 24 which can be expressed as xy = 24 Substituting x - 2 in for y gives: x(x-2) = 24 Distribute x2 - 2x = 24 Rearrange to a quadratic expression x2 - 2x - 24 = 0 This can be factored (x - 6)(x + 4) = 0 So either x = 6 or x = -4 So Lily must be 6 years old as her being -4 years old isn't a real possibility.

Mike is twice as old as Marc who is 4 years younger than Matt. If the three ages total 52 years, how old is Marc? 10 12 16 24

We can express each of the ages in terms of Marc's age (x) as follows: Marc = x Mike is twice as old as Marc so Mike = 2x Matt is 4 years older than Marc so Matt = x + 4 Their three ages Mike + Marc + Matt = 2x + x + (x+4) = 52 Simplify this equation to find x (Marc's age): 2x + x + (x + 4) = 52 4x + 4 = 52 Subtract 4 from both sides 4m = 48 Divide both sides by 4 m = 12 so Marc is 12 years old.