Question

For the given word problem, identify the rate of change. Gasoline at a particular gas station costs $2.78 per gallon. If Cory buys $18 of gas, how many gallons did he buy?

A) $2.78
B) $18
C) 1 gallon
D) $0.05

For the given word problem, identify the specific quantity. An environmental group is planting trees in a park. The group wants to plant 32 trees in all and has already planted 11 trees. If the group can plant 3 trees per hour, how long will it take it to finish?
A) 3
B) 11
C) t
D) 32

For the given equation, identify the value of the rate at which the equation is changing.
7x−3=32
A) 3
B) 7
C) x
D) 32

For the given equation, identify the initial quantity.
10x=132
A) x
B) 10
C) 0
D) 132

Which equation corresponds to the following word problem? An author writes 22 pages of her book each week. She has already written 58 pages and expects to have 280 pages in her first draft. How long will it take the author to finish her first draft?
A) 58w−22=280
B) 22w+58=280
C) 22w+280=58
D) 58w−280=22

Answer 1

The rate of change is $2.78 per gallon. Cory bought approximately 6 gallons of gas. It will take 8 hours to finish planting all the trees.

Step-by-step explanation:

For the first question, the rate of change is the cost of gasoline per gallon, which is $2.78. To find the number of gallons Cory bought, we can divide the total cost ($18) by the cost per gallon ($2.78). The answer is approximately 6.47 gallons, but since we can't buy a fraction of a gallon, Cory would have bought 6 gallons.

For the second question, the specific quantity is the time it takes to finish planting the remaining trees. The group has already planted 11 trees and wants to plant a total of 32 trees. If they can plant 3 trees per hour, we can subtract the trees already planted from the total trees and then divide by the rate of planting to find the time it will take. The answer is approximately 7.67 hours, but since we can't have partial hours, it will take 8 hours to finish planting all the trees.

The third question asks for the value of the rate of change in the given equation. The equation is 7x - 3 = 32. The coefficient of x is the rate of change, so the value is 7.

Finally, the fourth question asks for the initial quantity in the given equation. The equation is 10x = 132. The constant term in the equation is the initial quantity, so the value is 132.

Regarding the last question, the equation that corresponds to the word problem is D) 58w - 280 = 22. This equation represents the number of weeks it will take the author to finish her first draft, given that she writes 22 pages per week, has already written 58 pages, and expects to have 280 pages in her first draft.