Louisa and Kayla had $300. After Luisa had spent $112 and Kayla spent $40, 2/5 of Luisa's remainder is equal to 5/6 of Kayla's remainder. How much did Luisa have at first?
Let's solve this step by step.
1. Let's start by determining Luisa's remainder after spending $112. We subtract $112 from the original amount, which is what Luisa had at first.
Luisa's remainder = $300 - $112 = $188.
2. Next, we need to determine Kayla's remainder after spending $40. We subtract $40 from the original amount, which is what Kayla had at first.
Kayla's remainder = $300 - $40 = $260.
3. Now, we need to find 2/5 of Luisa's remainder and 5/6 of Kayla's remainder to set up the equation.
2/5 of Luisa's remainder = (2/5) * $188 = $75.20
5/6 of Kayla's remainder = (5/6) * $260 = $216.67 (rounded to the nearest cent).
4. The problem states that these two amounts are equal:
$75.20 = $216.67
5. However, these amounts are not equal. Therefore, there may be an error in the problem statement or the calculations.
Please double-check all the given information and calculations to ensure accuracy.
To solve this problem, let's break it down step by step:
1. First, let's find Luisa's remainder.
- Luisa initially had $300.
- She spent $112.
- Therefore, Luisa's remainder is $300 - $112 = $188.
2. Next, let's find Kayla's remainder.
- Kayla initially had $300.
- She spent $40.
- Therefore, Kayla's remainder is $300 - $40 = $260.
3. Now, let's set up the equation using the given information.
- We know that 2/5 of Luisa's remainder is equal to 5/6 of Kayla's remainder. This can be written as:
2/5 * Luisa's remainder = 5/6 * Kayla's remainder
4. Substitute the values of Luisa's and Kayla's remainders into the equation.
- 2/5 * $188 = 5/6 * $260
5. Solve the equation to find Luisa's initial amount.
- First, multiply both sides of the equation by the denominators to eliminate the fractions:
(2/5) * $188 * (6/5) = (5/6) * $260 * (6/5)
$75.20 = $312
6. Finally, Luisa initially had $312.
Therefore, Luisa initially had $312.
L+K = 300
2/5 (L-112) = 5/6 (K-40)
2/5 (L-112) = 5/6 (300-L-40)
L = 212