(UNIT 2) Algebra 1 exam prep

Which of the following represents "the average of 171 and x"?

(171 + x)/2

20% of 40 is what number?

0.20 x 40 = N 8 = N

A man earns $112 interest in one year on an investment of $1,400. What was his rate of interest?

R = $112 / $1400 which solves to a rate of 0.08 or multiplying it by 100 to make a percentage 8%

Reasonable solution

a solution which makes sense for the specific context or topic of the problem.

solution

a value or values that make a mathematical sentence true

A percent is a fraction whose denominator is 100.

always

literal equation

an equation containing more than one variable

Formulas

i = prt A = p + i i = interest p = principal (or number of dollars invested) r = rate of interest paid t = time the money is invested

i = $125 r = 6% t = 1 What is p?

$2,083.33

p = $300 r = 7% t = 2 What is i?

$42.00

The value in cents of 4 quarters and x dimes is _____.

100 + 10x

20 is 40% of what number?

20 = 0.40 x N 20 = 0.40N 20 ÷ 0.40 = N 50 = N

20 is what % of 40?

20 = N x 40 20/40= N 0.5 = N 0.5 = 50%

Sally has seven times as many dimes as nickels. Their value is $3.00. How many nickels does she have?

4 nickels

According to a magazine, a cleaning solution of 5% bleach will remove mildew from a shower or tub. How many ounces of bleach do you need to make a quart of 5% bleach solution? Explain the method you used using complete sentences.

5% bleach solution means 100 units of solution contains 5 units of bleach. So, one quart of bleach solution contains 5/100 quarts =0.05 quarts of bleach. 1 US liquid quart ≡ 32 US fluid ounce So, 0.05 quarts of bleach = 0.05×32 ounces of bleach 0.05 quarts of bleach = 1.6 ounces of bleach one quart of bleach solution contains 1.6 ounces of bleach.

A family travels, by plane, five hundred miles from their city to a beach town. Then they take a taxi from the airport to the hotel at the beach. When they ask the driver how far the airport is from the hotel, he tells them twenty kilometers. What is the approximate total distance, in miles, the family traveled? Recall that 1 kilometer is about 0.62 miles.

512 miles

A bank account has a beginning balance of $560.00. After 6 months, the balance in the account has increased to $572.60. What interest rate is being earned annually on this account?

572.6 - 560 = 12.6 i = prt 12.6 = (560 x 6/12)r 12.6 = 280r R = 12.6/280 = 0.045 0.045 x 100 = 4.5%

The perimeter of a rectangle is 68 inches. The perimeter equals twice the length of L inches, plus twice the width of 9 inches.

68 = 2L + 2(9)

Suppose Johnny invests $2,745 into an account, which has been earning interest for many years and he now has a total of $39,974. In two or more sentences explain why a negative number would/wouldn't be reasonable in the solution of the rate he received on his investment.

A negative number would not be reasonable in the solution of rate he received on his investment. So you can't have a negative rate received on the investment if the final amount is more than you started off with. This is because when you have a positive percent rate of a number, you take that percent of the number and add it to the original.

Solve the following problem. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit. The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the numbers.

Represent the unknowns using a variable: "the sum of three numbers is 26" x = first number, 2x = second number, 2x + 6 = third number Write the equation: x + 2x + 2x + 6 = 26 Solve the equation: 5x + 6 = 26 5x = 26 - 6 5x = 20 5x/5 = 20/5x = 4 4 is the first number, 8 is the second number, and 14 is the third number.

LeAnn wants to giftwrap a present she got for her little brother. How many square inches of giftwrap will be needed to cover a box that is 4 in × 6 in × 2 in? In your final answer, include all of your calculations.

The box is a cuboid, so there will be six faces, with only three different areas assume height is 2 in, length is 6 in and the depth is 4 in. height = 2 length = 6 depth = 4 height x length: 2 x 6 = 12 square in height x depth: 2 x 4 = 8 square in length x depth: 6 x 4 = 24 There are two of each of these faces, so multiply each result by two: 12 x 2 = 24 8 x 2 = 16 24 x 2 = 48 add the numbers together to find the total surface area of the cuboid: 24 + 16 + 48 = 88 square inches

A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?

They sold 104 boxes the first week, 109 boxes the second week, and 218 boxes the third week.

V.E.S.T

Variable, Equation, Solve, Try it.

equation

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

interest

a payment for the use of money borrowed or invested

How much of an alloy with 30% copper must be added to 25 pounds of a second alloy which is 20% copper to create a 27% alloy?

answer : 58.33 lbs Alloy 1: Let the weight of alloy 1 be "x" pounds. % of copper present in alloy 1 = 30% Amount of copper in alloy 1 = 30% of x = 0.3x Alloy 2: The weight of alloy 2 = 25 pounds % of copper present in alloy 2 = 20% Amount of copper in alloy 2 = 20% of 25 = (0.2 * 25) Alloy 3: Here we are given that alloy 1 and alloy 2 are mixed to create a mixture of 27% alloy. Amount of alloy 3 = 27% of (weight of alloy 1 + weight of alloy 2) = 0.27(x + 25) Since alloy 3 is a mixture of (0.3x) of copper in alloy 1 and (0.2*25) of copper in alloy 2, the equation is: (0.3)(x) + (0.2)(25) = (0.27)(x + 25) ⇒ 0.3x + 5 = 0.27x + 6.75 ⇒ 0.03x = 6.75 - 5 ⇒ x = 1.75 / 0.03 = 58.33 pounds or lbs.

A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.

beans that sell for 0.2 = t beans that sell for 0.68 = s total is 120 pounds: s + t = 120 cost: + 0.68s = 0.54 x 120 solve: 0.2t + 0.68s = 0.54 x 120 (0.2t + 0.68s) x 10 = (64.8) x 10 (2t + 6.8s)/2 = (648)/2t + 3.4s = 324 other equation: t + s = 120 multiply this equation by -1 and add to other equation: (-t - s= -120) + (t + 3.4s = 324) = 0t + 2.4s = 204 2.4s/2 = 204/2 s = 85 sub back: s + t = 85 t = 120 - 85 t = 35 35 pounds of the $0.20 variety 85 pounds of the 0.68 variety check: 35 x 0.20 + 85 x 0.68 7+57.8 = 64.8 120 x 0.54 = 64.8 64.8=64.8 My answer is reasonable, it makes sense for the context of the problem and after I have checked, the solution is correct. 35lb of $0.20 beans 85lb of $0.68 beans

Solve for c. ab + c = 5

c = 5 - ab

A car is traveling 50 miles per hour. How far will it travel in 4 hours?

d = rt d = 50 • 4 d = 200

Stacy and Travis are rock climbing. Stacy's rope is 4 feet shorter than 3 times the length of Travis' rope. Stacy's rope is 23 feet long. Write and solve an equation to find the length t of Travis' rope.

equation: 23 = 3t - 4. 23 = 3t - 4 23 + 4 = 3t 27 = 3t 27/3 = 3t/3 9 = t Travis' rope is 9 feet

Solve the following problem. It may be helpful to draw a chart on scrap paper to organize the information and write the equation. Be sure to show all steps (V.E.S.T.) and work in order to receive full credit. A clerk was asked to change a $10 bill. She returned 9 more dimes than nickels and twenty-one more quarters than dimes. How many coins of each did she return?

represent the unknown with a variable: Let the amount of nickels be: x the amount of money in nickles is: 5x in cents amount of dime is 9 more than nickles: x+9 the amount of money in dimes is: 10(x+9) in cents amount of quarters is 21 more than dimes: (x+9)+21=x+30 the amount of money in quarters is: 25(x+30) in cents they have a total of: $10.00 or 1000 in cents equation: 10(x+9) + x+30 + 25(x+30) solve for the variable: 5x +10(x+9) + 25(x+30) = 1000 5x + 10x + 90 + 25x + 750 = 1000 40x + 840 = 1000 40x + 840 - 840 = 1000 - 840 40x = 160 40x/40 = 160/40 x = 4 nickels: 4 dimes: 13 quarters: 34 To check add them together: $0.05(4) + $0.10(13) + $0.25(34) = $10.00 $0.20 + $1.30+ $8.50= $10.00

A decimal is a fraction that has a denominator of 100.

sometimes

principal

the amount of money invested or borrowed at a certain rate of interest

multiplicative inverse

the reciprocal of a number; if x is a number other than zero, then 1/x is the multiplicative inverse; the product of a number and its multiplicative inverse is 1

The length of a rectangle is 12 inches more than its width. What is the width of the rectangle if the perimeter is 42 inches?

x best represents the width of the rectangle. x + 12 best represents the length of the rectangle.

A plane flies x mph. How far can it go in y hours? Which expression represents this?

xy miles

Solve for y. x + a = yb

y = (x + a)/b