Question 1

A hospital treated a total of 18,360 dogs and cats last year. The hospital treated 1,376 more dogs than cats. How many cats were treated last year?

Accepted Answer

$$c = \frac{18,360 - 1,376}{2}$$

Question 2

A deck hand on a fishing boat has a rope that measures 89 feet. He needs to cut it into two pieces. The long piece must be 17 feet longer than the short piece. What is the length of the short piece?

Accepted Answer

$$x = \frac{89 - 17}{2}$$

Question 3

An airport reported the number of plane departures for three months. March had 50 more departures than January. July had 150 less than triple January. If the total for the three months was 2,250, how many departures were there in January?

Accepted Answer

$$j = \frac{2,250 - 100}{5}$$

Question 4

A small plot of land is a rectangle. The length is 7 meters longer than the width. The perimeter is 86 meters. What is the width?

Accepted Answer

$$w = \frac{86 - 14}{4}$$

Question 5

A social services worker compared the annual heating bills of three families. The first family's bill was $$360 more than the second's. The third family's bill was 200 $$less than double the second's. The total for all three was $$3,960. What equation represents this situation if x$ is the second family's bill?

Accepted Answer

$$(x + 360) + x + (2x - 200) = 3,960$$

Question 6

A farmer needs 720 meters of wire to enclose a triangular pasture. The first side is 30 meters less than the second side. The third side is half as long as the second side. If $$x is $$the length of the second side, what is the equation for the perimeter?

Accepted Answer

$$(x - 30) + x + (0.5x) = 720$$

Question 7

In a basketball game, the Vikings scored 12 points more than the Mustangs. The total score was 78 points. How many points did the Mustangs score?

Accepted Answer

$$m = \frac{78 - 12}{2}$$

Question 8

A rectangular garden has a length that is 7 meters more than its width. If the perimeter is 86 meters, what is the length of the garden?

Accepted Answer

$$l = \frac{86 - 14}{4} + 7$$

Question 9

A rope is cut into two pieces. The long piece is 17 feet longer than the short piece. If the total length is 89 feet, what is the length of the long piece?

Accepted Answer

$$x = \frac{89 + 17}{2}$$

Question 10

A social worker finds that the first family's heating bill is $$360 more than the second's, and the third family's bill is 200 $$less than double the second's. If the second family's bill is $900, what is the third family's bill?

Accepted Answer

$$2 	imes 900 - 200$$

Question 11

A triangle has sides of length $$x - 30$$, $$x$$, and $$0.5x. If $$the perimeter is 720 meters, what is the value of $$x$$?

Accepted Answer

Question 12

If the number of departures in March is 50 more than January, and July is 150 less than triple January, which expression gives the total departures for the three months?

Accepted Answer

$$j + (j + 50) + (3j - 150)$$

Question 13

A rectangular field has a width of $$w$$ meters and a length of $$w + 7$$ meters. If the perimeter is 86 meters, what is the equation for the perimeter?

Accepted Answer

$$2w + 2(w + 7) = 86$$

Question 14

A basketball team scored 12 points more than their opponent. If the total points scored was 78, how many points did the winning team score?

Accepted Answer

$$\frac{78 + 12}{2}$$

Question 15

A rope is cut into two pieces, with the long piece 17 feet longer than the short piece. If the short piece is $$x$$ feet, what is the equation for the total length?

Accepted Answer

$$x + (x + 17) = 89$$

Solving Word Problems: Comparisons (Beginning Algebra Study Notes)

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