Justin took 3 8 of the apples from a box wynne took 2 5 of the remaining apples if 51 apples were left how many apples were in the box at first?
Let's work through the problem step by step.
Justin took 3/8 of the apples from the box, which means there were 1 - 3/8 = 5/8 of the apples left in the box.
Wynne took 2/5 of the remaining apples, so there were 1 - 2/5 = 3/5 of the apples left after Justin took his portion.
We are told that 51 apples were left after Wynne took her portion. Let's represent the total number of apples in the box initially as x.
So, we have the equation:
(3/5) * (5/8) * x = 51
To simplify this equation, we can multiply both sides by (5/8):
3/5 * x = 51 * 8/5
3/5 * x = 408/5
Next, multiply both sides by (5/3) to isolate x:
(5/3) * (3/5) * x = (408/5) * (5/3)
x = 408/3
x = 136
Therefore, there were initially 136 apples in the box.
Let's solve the problem step by step:
Step 1: Justin took 3/8 of the apples from the box.
Let's represent the total number of apples in the box as "x".
The number of apples Justin took can be calculated as (3/8)x.
Step 2: After Justin took the apples, the remaining number of apples in the box will be x - (3/8)x, which simplifies to (5/8)x.
Step 3: Wynne took 2/5 of the remaining apples.
The number of apples Wynne took can be calculated as (2/5) * (5/8)x, which simplifies to (1/4)x.
Step 4: The number of apples left after Wynne took some is 51.
So, (1/4)x = 51.
Step 5: To find the value of x, we can solve the equation (1/4)x = 51.
Multiplying both sides of the equation by 4, we get x = 204.
Therefore, there were 204 apples in the box initially.
To solve this problem, we can break it down into steps.
Step 1: Find out how many apples Justin took.
Justin took 3/8 of the apples from the box. Let's assume there were x apples in the box initially. So, Justin took (3/8) * x apples.
Step 2: Calculate the number of apples remaining after Justin took his share.
The number of apples remaining in the box after Justin took his share will be (x - (3/8) * x) apples.
Step 3: Determine how many apples Wynne took.
Wynne took 2/5 of the remaining apples. So, she took (2/5) * (x - (3/8) * x) apples.
Step 4: Calculate the number of apples left in the box.
The number of apples left in the box will be (x - (3/8) * x) - (2/5) * (x - (3/8) * x) apples.
Step 5: Set up an equation to solve for x.
Given that there were 51 apples left in the box, we can set up the equation:
(x - (3/8) * x) - (2/5) * (x - (3/8) * x) = 51
Step 6: Solve the equation for x.
Let's solve the equation:
(x - (3/8) * x) - (2/5) * (x - (3/8) * x) = 51
Simplifying the equation:
[(8/8) * x - (3/8) * x] - [(5/5) * x - (15/40) * x] = 51
[(8 - 3)/8 * x] - [(5 - 15/40) * x] = 51
(5/8 * x) - [(5 - 15)/40 * x] = 51
(5/8 * x) - (10/40 * x) = 51
(5/8 * x) - (1/4 * x) = 51
(20x - x)/32 = 51
19x/32 = 51
Multiplying both sides by 32:
19x = 51 * 32
19x = 1632
Dividing both sides by 19:
x = 1632/19
x ≈ 85.895
Therefore, there were approximately 86 apples in the box initially.