A grocer had some apples. He packed 7/9 of the apples into 42 bags and the rest into 4 boxes. Each box had 34 more apples than each bag. How many apples did the grocer pack in each bag?
7/9 divided by 42 = 1/54 in each bag
2/9 divided by 4 = 1/18 in each box
that means that
1/18 x = 1/54 x + 34
x = 918
so each bag had 918/54 = 17 apples
To solve this problem, we can break it down into steps:
Step 1: Find the total number of apples.
Let's say the total number of apples the grocer had is 'x.'
Step 2: Calculate the number of apples packed in bags.
The grocer packed 7/9 of the apples into 42 bags. So we can express this as (7/9) * x = 42.
To find the number of apples packed in each bag, we can use the following steps:
Step 3: Solve for x.
To find the value of 'x,' we multiply both sides of the equation by (9/7) to cancel out the fraction: x = (42 * 9) / 7.
Step 4: Substitute the value of 'x' back into the equation.
Now that we know the value of 'x,' we can substitute it back into the original equation to find the number of apples packed into each bag: (7/9) * (42 * 9) / 7.
Simplifying the expression, we get:
(7/9) * (42 * 9) / 7 = (7 * 6) = 42 apples.
Therefore, the grocer packed 42 apples into each bag.
Let's solve this step by step:
Step 1: Find the total number of apples the grocer had
Let's assume the number of apples the grocer had is "x".
Step 2: Calculate the number of apples packed into bags
The grocer packed 7/9 of the apples into bags, so the number of apples packed into bags is (7/9) * x.
Step 3: Calculate the number of apples packed into boxes
The grocer packed the rest of the apples into boxes, which is (2/9) * x (since 7/9 + 2/9 = 9/9 or 1, and we assumed the total number of apples as x).
Step 4: Calculate the number of bags
We know that the number of bags is equal to 42.
Step 5: Calculate the number of boxes
We know that the number of boxes is equal to 4.
Step 6: Calculate the number of apples in each box
We are given that each box had 34 more apples than each bag. So, the number of apples in each box is ((7/9) * x) / 4 + 34.
Step 7: Equate the number of bags and boxes
We can set up an equation: 42 * ((7/9) * x) = 4 * (((7/9) * x) / 4 + 34).
Step 8: Solve the equation
Let's solve the equation to find the value of x.
42 * ((7/9) * x) = 4 * (((7/9) * x) / 4 + 34)
(42/1) * ((7/9) * x) = (4/1) * (((7/9) * x) / 4 + 34)
(42/1) * ((7/9) * x) = (((7/9) * x) + 34) * 4
(42/1) * ((7/9) * x) = ((7/9) * x) * 4 + 34 * 4
Step 9: Simplify the equation
Now we can simplify the equation further:
((42/1) * (7/9) * x) - ((7/9) * x) * 4 = 34 * 4
(294/9) * x - (28/9) * x = 136
(294 - 28)/9 * x = 136
266/9 * x = 136
Step 10: Solve for x
To solve for x, we multiply both sides of the equation by 9/266:
(9/266) * (266/9) * x = (9/266) * 136
x = (9/266) * 136
Step 11: Calculate x
Now we can calculate the value of x:
x = (9/266) * 136
x = 4.65 (approximately)
Therefore, the grocer had approximately 4.65 apples.
Step 12: Calculate the number of apples in each bag
We can substitute the value of x in the equation for the number of apples in each bag:
Number of apples in each bag = (7/9) * x
Number of apples in each bag = (7/9) * 4.65
Number of apples in each bag = 3.65 (approximately)
Therefore, the grocer packed approximately 3.65 apples in each bag.