Act Algebra Math Review

Evelyn is trying to balance her budget. She realizes that she needs to adjust her expenses by adding $12 to both sides of her budget equation to solve for x . Which equation is she working with?

Answer explanation

To isolate x in the equation 13 = 5y - 12, you would add 12 to both sides, resulting in 25 = 5y. This step is necessary to eliminate the -12 from the right side.

Tags

CCSS.HSA.REI.A.1

Which of the following equations does not have x = 2 as a solution?

Answer explanation

To check which equation does not have x = 2 as a solution, substitute x = 2 into each equation. The equation 3x - 2 = -8 gives 3(2) - 2 = 6 - 2 = 4, which is not equal to -8. Thus, it does not have x = 2 as a solution.

Tags

CCSS.6.EE.B.5

Michael is buying packs of pencils. Each pack contains 2 pencils. Write an algebraic expression for the total number of pencils Michael buys if he buys q packs.

• 2 x q

• 2 + q

• q - 2

Answer explanation

The question asks for the product of 2 and q, which means we need to multiply them. The correct algebraic expression for this is 2 x q, as it represents multiplication. The other options do not represent a product.

Tags

CCSS.HSA-SSE.A.1A

Elijah has 7 apples. He gives away n apples. Write an algebraic expression for the number of apples Elijah has left.

• 7 - n

• n -7

• n x 7

Answer explanation

The phrase 'n less than 7' means we subtract n from 7, which gives us 7 - n. However, the correct interpretation is n - 7, indicating how much less n is than 7. Thus, the correct answer is n - 7.

Tags

CCSS.HSA-SSE.A.1A

Mia has 8 more apples than Oliver. If Oliver has 36 apples, how many apples does Mia have?

• 28

• 36

• 44

• 40

Answer explanation

To evaluate w + 8 when w = 36, substitute 36 for w: 36 + 8 = 44. Therefore, the correct answer is 44.

Tags

CCSS.1.OA.A.1

Emma is buying notebooks. Each notebook costs 2 dollars, and she also buys 3 packs of pens, each costing 5 dollars. If she spends a total of 47 dollars, how many notebooks did she buy?

• 11 notebook

• 12 notebooks

• 13 notebooks

• 16 notebooks

Answer explanation

To solve 2x + 3(5x - 7) = 47, first distribute: 2x + 15x - 21 = 47. Combine like terms: 17x - 21 = 47. Add 21 to both sides: 17x = 68. Divide by 17: x = 4. Thus, the correct answer is x = 4.

Tags

CCSS.7.EE.B.4A

Mia is moving into a campus dormitory. The student rents a moving truck for $20 plus $2 per mile. Before returning the truck, Mia fills the tank with gasoline, which costs $30. The total cost is $150. How many miles did Mia drive the truck?

• 200 miles

• 100 miles

• 50 miles

• 75 miles

Answer explanation

The total cost is $150. The truck rental is $20 plus $2 per mile, and gasoline costs $30. So, $150 - $20 - $30 = $100 for miles. Dividing $100 by $2 per mile gives 50 miles. Thus, the student drove 50 miles.

Tags

CCSS.7.EE.B.4A

After selling 27 tickets each to two large groups of tourists for the circus, Adam had 53 tickets remaining. Which equation can be used to find how many tickets, c, Adam had before selling some of the tickets?

• c - 27 = 53

• c + 2(27) = 53

• c - 2(27) = 53

• c + 27 = 53

Answer explanation

Adam sold 27 tickets to two groups, totaling 54 tickets. To find the original number of tickets, we subtract the tickets sold from the remaining tickets: c - 54 = 53, which simplifies to c - 2(27) = 53.

Tags

CCSS.HSA.CED.A.3

Arjun has a rope that is divided into 4 equal parts, and each part is -8 meters long. What is the first step Arjun should take to find the total length of the rope?

• Multiply both sides by 4

• Divide both sides by 4

• Add 4 to both sides

• Subtract 4 from both sides

Answer explanation

To isolate x in the equation x/4 = -8, the first step is to eliminate the fraction. You do this by multiplying both sides by 4, which gives you x = -32.

Tags

CCSS.HSA.REI.A.1

Charlotte earns money by babysitting. For every hour she works, she earns a certain amount of money. What is the constant of proportionality?

• $3

• $4

• $2

• $9

Answer explanation

The constant of proportionality is the ratio between two quantities. In this case, the correct answer is $9, indicating that for every unit increase in one quantity, the other increases by $9.

Tags

CCSS.7.RP.A.2B