Jeffrey spent 1/2 of his money on a pair of shoes and 1/3 of the remainder on a wallet. After he spent $6.95 on lunch, he had $20.85 left. How much did Jeffrey have at first?
Solution: Let jeffery have $x at first
given jeffery spent 1/2 of money
in a pain of shoes
ie; $x/2 on pair of shoes
and 1/3 of the remainder on a wallet
ie; money spent in wallet = (x - x/2)1/3
= $x/2
he spent $6.55 on lunch.
Now remaining balance he have $20.85
so to find the value of x.
As, x = x/2 + x/6 + 6.95 + 20.85
= 3x+x/6 + 27.80
= 4x/6 + 27.80
x = 2x/3 + 27.80
x - 2x/3 = 27.8
x/3 = 27.8
x = $83.4
So; Jeffery had $83.4 at first.
To find out how much Jeffrey had at first, we need to work backwards. Let's start with the information we have:
We know that after spending $6.95 on lunch, Jeffrey had $20.85 left. So, the amount he had before spending on lunch was the sum of the money he had left and the lunch expense:
Amount before lunch = $20.85 + $6.95
Next, we know that 1/3 of the remainder after buying the shoes was spent on a wallet. So, the remainder after buying the shoes can be found by dividing the amount before lunch by 1/3:
Remainder after shoes = (Amount before lunch) ÷ (1/3)
Finally, we know that Jeffrey spent 1/2 of his money on shoes. So, the amount he had originally can be found by dividing the remainder after buying the shoes by 1/2:
Amount originally = (Remainder after shoes) ÷ (1/2)
By following these steps, we can find out how much Jeffrey had at first. Let's calculate:
Amount before lunch = $20.85 + $6.95 = $27.80
Remainder after shoes = $27.80 ÷ (1/3) = $27.80 × 3 = $83.40
Amount originally = $83.40 ÷ (1/2) = $83.40 × 2 = $166.80
Therefore, Jeffrey had $166.80 at first.