Distributive Property Word Problems (Unit Rates Included)

Simplify the expression: 3(x + 2) - 4(x - 1)

• -3x + 2

• x + 10

• -x + 6

• -x + 10

Answer explanation

To solve this, distribute the 3 and -4 into their respective parentheses. This gives 3x + 6 - 4x + 4. Combine like terms to get -x + 10. Thus, the simplified expression is -x + 10.

Tags

CCSS.6.EE.A.3

A store sells 5 packs of pencils for $3 each and 4 packs of erasers for $2 each. How much does a customer spend if they buy 2 packs of pencils and 3 packs of erasers?

• $12

• $14

• $10

• $8

Answer explanation

The question provides the price for packs of pencils and erasers. The customer buys 2 packs of pencils and 3 packs of erasers. Calculating the total purchase, 2 packs of pencils cost $6 (2*3) and 3 packs of erasers cost $6 (3*2). Hence, the total expense is $6 (for pencils) + $6 (for erasers) = $12. Therefore, the correct answer is $12.

Tags

CCSS.3.OA.D.8

Simplify the expression: 2(3x - 4) + 5(2x + 1)

• 16x - 3

• 16x + 3

• 16x - 7

• 6x - 3

Answer explanation

To simplify the given mathematical expression in the question, apply the distributive property: 2*3x - 2*4 + 5*2x + 5*1. This simplifies to 6x - 8 + 10x + 5 = 16x - 3. Therefore, the correct answer is '16x - 3'.

Tags

CCSS.6.EE.A.3

A bakery sells 2 dozen donuts for $8 each and 3 dozen bagels for $6 each. How much does a customer spend if they buy 4 dozen donuts and 2 dozen bagels?

• $80

• $120

• $100

• $140

Answer explanation

The question states that two dozen donuts cost $8 each and three dozen bagels cost $6 each. Therefore, if the customer buys four dozen donuts, it would cost 4*8 = $32. If the customer buys two dozen bagels, it would cost 2*(6/3)*2 = $8. Thus, the total expense is $32+$8 = $40, making the correct answer $100.

Tags

CCSS.7.EE.B.3

Simplify the expression: 4(2x + 3) - 2(3x - 1)

• 2x + 14

• 10x + 6

• 6x + 12

• 8x + 10

Answer explanation

The question asks to simplify the expression: 4(2x + 3) - 2(3x - 1). Start by distributing in both parentheses, which gets you 8x + 12 - 6x + 2. Combining like terms, 8x - 6x becomes 2x and 12 + 2 becomes 14. So the simplified expression is 2x + 14.

Tags

CCSS.6.EE.A.3

A toy store sells 3 sets of action figures for $10 each and 2 sets of board games for $15 each. How much does a customer spend if they buy 5 sets of action figures and 4 sets of board games?

• $10 * 5 + $15 * 4 = $50 + $60 = $110

• $10 * 3 + $15 * 4 = $30 + $60 = $90

• $10 * 5 + $15 * 3 = $50 + $45 = $95

• $10 * 4 + $15 * 5 = $40 + $75 = $115

Answer explanation

The question asks for the total expenditure when a customer buys 5 sets of action figures and 4 sets of board games. Each set of action figures costs $10 and each set of board games costs $15. So, total cost would be (5 * $10) for action figures and (4 * $15) for board games. That comes to $50 + $60 = $110, which matches with the correct answer.

Tags

CCSS.7.EE.B.3

Simplify the expression: 5(2x - 3) + 3(4x + 2)

• 10x - 9

• 22x - 9

• 22x + 9

• 22x + 3

Answer explanation

The question asks to simplify the algebraic expression. Distributing 5 to '2x - 3' and 3 to '4x + 2' gives 10x - 15 and 12x + 6 respectively. Adding these two expressions gives us 22x - 9, which is the correct answer.

Tags

CCSS.6.EE.A.3

A clothing store sells 4 shirts for $12 each and 3 pairs of pants for $20 each. How much does a customer spend if they buy 3 shirts and 2 pairs of pants?

• $52

• $64

• $76

• $80

Answer explanation

The question asks how much a customer would spend if they bought 3 shirts and 2 pairs of pants. The cost of a shirt is $12 and a pair of pants is $20. Therefore, the total cost for 3 shirts would be 3*$12=$36 and for 2 pairs of pants 2*$20=$40. Adding these together, the customer would spend $76.

Tags

CCSS.7.EE.B.3

Simplify the expression: 2(3x + 4) - 3(2x - 1)

• 11

• -5

• 14

• 6x + 5

Answer explanation

The given question is a simple algebraic expression. Begin by multiplying each term inside the parentheses by the number outside. For the first part, 2*3x gives 6x and 2*4 gives 8, making it 6x+8. Do the same for the second part to get 3*2x as 6x and 3*-1 as -3, which simplifies to -6x+3. Subtract the two results to get 0x+11, which simplifies to 11, the correct answer.

Tags

CCSS.6.EE.A.3

A grocery store sells 6 bags of apples for $5 each and 5 bags of oranges for $3 each. How much does a customer spend if they buy 2 bags of apples and 4 bags of oranges?

• $22

• $14

• $20

• $18

Answer explanation

The question is asking for the total cost if a customer buys 2 bags of apples and 4 bags of oranges. The cost for 2 bags of apples is 2*5=$10 and the cost for 4 bags of oranges is 4*3=$12. Adding these two amounts together gives a total cost of $10+$12=$22. Thus, the correct choice is $22.

Tags

CCSS.3.OA.D.8