Problem Solving

BTGmoderatorDC wrote: ↑

Fri Dec 30, 2022 7:14 am

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

A. $2.40
B. $3.00
C. $3.20
D. $3.60
E. $4.80


OA B

Source: Magoosh

Let w = John’s weekly allowance

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade
If John spent 3/5 of his allowance, then he has 2/5 REMAINING
So, (2/5)(w) = allowance REMAINING

The next day he spent one third of his remaining allowance at the toy store
If he spent 1/3, then he has 2/3 REMAINING
So, (2/3)(2/5)(w) = allowance REMAINING

Once all of this is done, John has $0.80 REMAINING
So (2/3)(2/5)(w) = 0.8
Simplify: (4/15)(w) = 0.8
Multiply both sides by 15 to get: 4w = 12
Divide both sides by 4 to get: w = 3

Answer: B

Cheers,
Brent

BTGmoderatorDC wrote: ↑

Fri Dec 30, 2022 7:14 am

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.80 at the candy store. What is John’s weekly allowance?

A. $2.40
B. $3.00
C. $3.20
D. $3.60
E. $4.80


OA B

Source: Magoosh

Solution:

We can let n = the weekly allowance and create the equation:

(3/5)n + 1/3(2/5)n + 0.8 = n

3n/5 + 2n/15 + 0.8 = n

Multiplying by 15, we have:

9n + 2n + 12 = 15n

12 = 4n

3 = n

Answer: B