Question

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.

Answer 1

Explanation:

we have 2 variables :

x = cost per pound of belly beans

y = cost per pound of almonds

to find the solution of 2 variables, we need 2 equations with these variables.

luckily we got them via the 2 given examples :

3x + 5y = $25

12x + 2y = $37

the best to solve this is via elimination. that means we multiply both equations with fitting factors and then add the results, so that one of the 2 variables is not showing in the result, and we can solve for the remaining variable.

with that result we go into one of the original equations and solve for the second variable.

I suggest we multiply the first equation by -4, and the second one just by 1. and then we get

-12x - 20y = -100

12x + 2y = 37

--------------------------

0 -18y = - 63

y = -63/-18 = $3.50

let's use the second original equation (seems to have the nicest factor numbers) :

12x + 2×3.5 = 37

12x + 7 = 37

12x = 30

x = 30/12 = 5/2 = $2.50

1 pound of jelly beans costs $2.50.

1 pound of almonds costs $3.50.

Answer 2

change tge jelly bean and almond into 2 different unknown.

then, change it into simple mathematics equation.

x represent jelly bean while y represent almond.

Next , came up with 3x + 5y =25 (equation 1) & 12x +2y =37 (equation 2).

use the elimination method to solve this problem.

refer to the picture of how the equation being solve