Math Quiz 2.3

Jack is now seven times as old as James. In 5 years, Jack will be five times as old as James. How old is James now?

10

A set contains three consecutive numbers. The sum of these three numbers is 54. What are the three numbers?

17, 18, 19

Four-fifths of a number equals 16. Find the number.

20

Three times a number is the same as 28 more than 6 times the number. Find the number. If n is "the number," which equation could be used to solve for the number?

3 n = 6 n + 28

John's age is 9 more than three times Rick's age. Which expression represents this?

3x + 9

The sum of two consecutive integers is 31. Find the numbers. How would you write this equation?

Choose a variable to represent one of the unknowns: Let x = smaller integer. The next integer is x + 1. Write an equation using the relationship "their sum is 31." x + (x +1) = 31 or 2x + 1 = 31.

a mathematical sentence whose verb is 'equal' (=)

Equation

Joe and Mary have 48 books about animals, and Joe has twelve more books than Mary. How many books does each have? How would we write this equation?

J + M = 48 J = M + 12 (M + 12) + M = 48. Simplify: 2M + 12 = 48.

Three times a number, increased by five is 12. Find the number.

Let n represent "a number." "Three times a number" translates to 3n. "increased by 5" tells us to add 5: 3n + 5. "is 12" tells us that 3n + 5 equals 12: 3n + 5 = 12.

George has $12, which is $7 more than Tom has. How much money does Tom have?

Represent the unknown with a variable: Let x be the amount of money Tom has (since his amount is unknown). Equation: x + 7 = 12 Solve for the variable: x + 7 - 7 = 12 - 7 x = 5 Tom has 5 dollars. Check the answer: 5 + 7 = 12 12 = 12 It checks in the equation, but also make sure it checks (or makes sense) in the problem. If Tom has $5 and George has $12, then George does have $7 more than Tom.

The width of a rectangle is 9 ft. The length of the rectangle is a multiple of 9. The area is 324 sq ft. Find the length.

Represent the unknowns with a variable: Let 9x be the length of the rectangle (a multiple of nine will take the form 9x). Equation: 9(9x) = 324 Solve for the variable: 9(9x) = 324 81x = 324 x = 4 The length of the rectangle is 9(4)= 36 ft. Check: 9(9 * 4) = (?) 324 9(36) = (?) 324 324 = 324 36 x 9 = 324 36 is a multiple of 9 sq ft

V.E.S.T.

Variable Equation Solve Try it

Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds. How much does Tom weigh?

n + (n − 30) = 210 Tom weighs 120 pounds, and Jim weighs 90 pounds.

The sum of three numbers is 73. The second number is equal to the first number diminished by 7. The third number is five times the first. What are the numbers? Which three expressions could be used to represent the numbers?

n; n - 7; 5 n

a letter or symbol used to represent an unknown

variable