Question

For 5 pounds of almonds and 2 pounds of jelly beans the total cost is $10. For 3 pounds of almonds and 8 pounds of jelly beans the total cost is $23. Find the cost of each pound of almonds and jelly beanss

Answer 1

A pound of Almonds cost $1 and a pound of jelly beans cost $2.50. Step-by-step explanation:

Step 1; First we convert the given costs into separate equations. Assume 1 pound of almonds costs $x and 1 pound of jelly beans costs $y. Keep the known costs on the right side and the unknown ones on the left. By doing this we get the following equations

5x + 2y = 10, take this as equation 1

3x+ 8y = 23, take this as equation 2

Step 2; We multiply equation 1 with 3 and equation 2 with 5 so we can cancel out the variable x in both equations. By doing this we get

15x + 6y = 30, take this as equation 3

15x + 40y = 115, take this as a equation 4

If we subtract 4 with 3, we cancel out the x variable and can calculate the value of y.

-34y = -85 , y = -85/-34 = $2.50

Step 3; Substituting this value of y in any of the previous equations we will get x's value. Here this value of y is substituted in equation 2.

3x + 8(2.50) = 23, 3x + 20 = 23 , 3x = 3, x=1.

So 1 pound of almonds cost $1 and 1 pound of jellybeans cost $2.50.