A store is having a sale on jelly beans and almonds. For 3 pounds of jelly beans and 5 pounds of almonds, the total cost is $25. For 12 pounds of jelly beans and 2 pounds of almonds, the total cost is $37. Find the cost for each pound of jelly beans and each pound of almonds.
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To solve this problem, we can set up a system of equations based on the given information. Let's denote the cost of one pound of jelly beans as "x" dollars, and the cost of one pound of almonds as "y" dollars.
From the first statement, we know that 3 pounds of jelly beans and 5 pounds of almonds cost $25. Using the given values, we can write the equation:
3x + 5y = 25 ---(Equation 1)
From the second statement, we know that 12 pounds of jelly beans and 2 pounds of almonds cost $37. We can similarly write the equation:
12x + 2y = 37 ---(Equation 2)
Now, we have two equations with two variables (x and y). To solve this system of equations, we can use the method of substitution or elimination.
Let's solve this system of equations using substitution:
First, let's solve Equation 1 for x:
3x = 25 - 5y
x = (25 - 5y)/3
Now, substitute the value of x in Equation 2:
12((25 - 5y)/3) + 2y = 37
Simplify the equation further:
(100 - 20y)/3 + 2y = 37
100 - 20y + 6y = 111
100 - 14y = 111
-14y = 111 - 100
-14y = 11
y = -11/14
y = -0.79
Now, substitute the value of y into Equation 1 to find x:
3x + 5(-0.79) = 25
3x - 3.95 = 25
3x = 25 + 3.95
3x = 28.95
x = 28.95/3
x = 9.65
Therefore, the cost for each pound of jelly beans is approximately $9.65, and the cost for each pound of almonds is approximately $0.79.
3j + 5a = 25
12j + 2a = 37
1st time 4
12j + 20a = 100
subtract the 2nd
18a = 63
a = 3.5
sub into the original 1st to get j