Question

Last year, the volleyball team paid $5 pair for socks and $17 per pair for shorts on a total purchase of $315. This year they spent $342 to buy the same number of socks and shorts, because the socks now cost $6 a pair and the shorts cost $18. How many pairs of socks and shorts did team buy each year? A ) 14 pairs of socks and 14 pairs of shorts B) 15 pairs of socks and 12 pairs of shorts C) 13 pairs of socks and 14 pairs of shorts D) 12 pairs of socks and 12 pairs of shorts E) 12 pairs of socks and 15 pairs of shorts

Answer 1

Answer:

Option E is correct.

12 pairs of socks and 15 pairs of shorts did team buy each year.

Step-by-step explanation:

Let the number of pairs of socks be x and the number pairs of shorts be y.

As per the statement:

Last year, the volleyball team paid $5 pair for socks and $17 per pair for shorts on a total purchase of $315.

⇒$5x+17y = 315$                   .....[1]

It is also given that: This year they spent $342 to buy the same number of socks and shorts, because the socks now cost $6 a pair and the shorts cost $18.

⇒$6x + 18y = 342$                   .....[2]

Multiply equation [1] by 6 both sides we get;

$30x+102y = 1890$                 .......[3]

Multiply equation [2] by 5 both sides we get;

$30x +90y = 1710$                   .....[4]

Subtract equation [4] from [3] we get;

$12y =180$

Divide both sides by 168 we get;

y = 15

Substitute the given values of y =15 in [1] we get;

5x+17(15) = 315

5x + 255 = 315

Subtract 255 from both sides we get;

5x = 60

Divide both sides by 5 we get;

x = 12

Therefore, 12 pairs of socks and 15 pairs of shorts did team buy each year.