A farmer grows 196 pounds of potatoes.He sells them to a grocery who divides them into 5 pound and 2 pound bags.If the grocery uses the same number of 5 pound and 2 pound bags,how many bags of each did he use?
5n+2n=196
n= 196/7
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To determine the number of 5-pound and 2-pound bags used by the grocery, we can solve a system of equations.
Let's assume the number of 5-pound bags used is represented by 'x', and the number of 2-pound bags used is represented by 'y'.
Since the grocery uses the same number of 5-pound and 2-pound bags, we can write the equation: x = y.
Now, let's consider the weight of the bags. Each 5-pound bag weighs 5 pounds, and each 2-pound bag weighs 2 pounds.
We know the farmer grew 196 pounds of potatoes, so we can write the equation: 5x + 2y = 196.
Now we have a system of equations:
x = y
5x + 2y = 196
To solve the system of equations, we can substitute the value of 'x' from the first equation into the second equation.
Substituting x = y into the second equation, we get:
5(y) + 2y = 196
5y + 2y = 196
7y = 196
y = 196 / 7
y = 28
Now that we know y = 28, we can substitute this value back into the first equation to find x:
x = y
x = 28
So, the grocery used 28 bags of potatoes weighing 2 pounds each, and 28 bags of potatoes weighing 5 pounds each.