Question

Faber Kozlowski had 6 times as much money as Theriault Luigi. After Faber Kozlowski spent 1/3 of his money and Theriault Luigi spent 4/5 of his money, they had a total of $1155 left.

(a) How much money did Faber Kozlowski and Theriault Luigi have altogether at first?

(b) Theriault Luigi spent 3/4 of his remaining money on a hoodie. What fraction of his original amount of money did he spend on the hoodie?

Answer 1

Explanation:

Let's use variables to represent the amount of money each person had at first.

Let x be the amount of money that Theriault Luigi had.

Then, according to the problem, Faber Kozlowski had 6 times as much money as Theriault Luigi, which means Faber Kozlowski had 6x dollars.

After Faber Kozlowski spent 1/3 of his money, he had 2/3 of his money left, which is (2/3)(6x) = 4x dollars.

After Theriault Luigi spent 4/5 of his money, he had 1/5 of his money left, which is (1/5)x dollars.

Together, they had a total of $1155 left, which means:

4x + (1/5)x = 1155

Multiplying both sides by 5 to eliminate the fraction gives:

20x + x = 5775

Combining like terms gives:

21x = 5775

Dividing both sides by 21 gives:

x = 275

Therefore, Theriault Luigi had $275 at first, and Faber Kozlowski had 6 times as much, which is $1650 at first.

So, the answer to (a) is $275 + $1650 = $1925.

For (b), Theriault Luigi spent 3/4 of his remaining money on a hoodie, which means he spent (3/4)(1/5)x = 3/20 of his original amount of money on the hoodie.

Therefore, Theriault Luigi spent 3/20 of his original amount of money on the hoodie.

Answer 2

(a) $1925

(b) 15%

Explanation:

(a)

Let f = original amount of money Faber had.

Let t = original amount of money Theriault had.

"Faber Kozlowski had 6 times as much money as Theriault Luigi. "

f = 6t

"After Faber Kozlowski spent 1/3 of his money"

He has now: 2/3 f

"and Theriault Luigi spent 4/5 of his money"

He has now: 1/5 t

"they had a total of $1155 left"

2/3 f + 1/5 t = 1155

f = 6t

2/3 f + 1/5 t = 1155

2/3 (6t) + 1/5 t = 1155

4.2t = 115

t = 1155/4.2

t = 275

f = 6t = 6(275) = 1650

f + t = 275 + 1650 = 1925

Part (a) answer: $1925

(b)

Original amount: t = 275

He first spent 4/5 of the original amount, so he had 1/5 left.

275/5 = 55

He spent 3/4 of $55 on the hoodie.

3/4 × $55 = $41.25

$41.25/$275 × 100% = 15%

Part (b) answer: 15%