William spent $384 to buy some T-shirts and shorts. The cost of a pair of shorts was $12 and a T-shirt cost $3 more than the shorts. If the number of shorts he bought was 3/4 as many as the number of T-shirts, how much did he spend on the T-shirts?

Question

William spent $384 to buy some T-shirts and shorts. The cost of a pair of shorts was $12 and a T-shirt cost $3 more than the shorts. If the number of shorts he bought was 3/4 as many as the number of T-shirts, how much did he spend on the T-shirts?

Answer 1

Let's call the number of pairs of shorts William bought "s" and the number of T-shirts he bought "t".

We know that the cost of a pair of shorts is $12, so William spent 12s dollars on shorts.

We also know that the cost of a T-shirt is $3 more than the cost of a pair of shorts. So the cost of a T-shirt is $12 + $3 = $15. Therefore, William spent 15t dollars on T-shirts.

We're told that he bought 3/4 as many shorts as T-shirts, or s = (3/4)t.

We can use this information to set up an equation:

12s + 15t = 384

Substitute s = (3/4)t:

12(3/4)t + 15t = 384

9t + 15t = 384

24t = 384

t = 16

So William bought 16 T-shirts. We can use this to find the number of shorts he bought:

s = (3/4)t = (3/4)(16) = 12

William bought 12 pairs of shorts.

Now we can find how much he spent on T-shirts:

15t = 15(16) = $240

Therefore, William spent $240 on T-shirts.

Answer 2

Let's first find the number of shorts William bought.

Let's assume the number of T-shirts William bought is "x".

According to the given information, the number of shorts is 3/4 of the number of T-shirts:
Number of Shorts = 3/4 * Number of T-shirts = (3/4) * x = 3x/4

We know that the cost of a pair of shorts is $12.
So, the total cost of shorts = Number of Shorts * Cost of a Pair of Shorts = (3x/4) * 12 = 36x/4

We also know that the cost of a T-shirt is $3 more than the cost of the shorts.
So, the cost of a T-shirt = Cost of a Pair of Shorts + $3 = 12 + 3 = $15

The total cost of T-shirts = Number of T-shirts * Cost of a T-shirt = x * 15 = 15x

The total amount spent by William is $384.

Therefore, the equation becomes:
Total Amount spent = Total cost of T-shirts + Total cost of Shorts
384 = 15x + 36x/4

To simplify the equation, let's multiply every term by 4 to get rid of the denominator:
4 * 384 = 15x * 4 + 36x

1536 = 60x + 36x

96x = 1536

Dividing both sides of the equation by 96:
x = 1536/96

x = 16

So, he bought 16 T-shirts.

Now, let's calculate the total cost of T-shirts:
Total cost of T-shirts = Number of T-shirts * Cost of a T-shirt
Total cost of T-shirts = 16 * 15 = $<<16*15=240>>240

Therefore, William spent $240 on T-shirts.