Algebra word problem

Question

A store is having a sale on almonds and jelly beans. For 2 pounds of almonds and 12 pounds of of beans, the total cost is 47 For 5 pounds of almonds and 3 pounds of jelly beans, the total cost 23 Find the cost for each pound of almonds and each pound of jelly

Answer 1

Let’s say that almonds cost $A per pound, and jelly beans cost $B per pound

Then the sentence “For 2 pounds of almonds and 12 pounds of of beans, the total cost is 47”

can be written algebraically as 2A + 12B = 47. Similarly, the next sentence can be written as 5A + 3B = 23.

Since both of these conditions must be true, we have a system of linear equation.

Let’s multiply the second equation by 4 ——-> 20A + 12B = 92

Now let’s subtract the first equation from it (elimination method)

The result will be 18A = 45 or A = 2.5

If we substitute A with 2.5 in any of the original equations, we’ll get B.

2 A + 12B = 47 —-> 2 x 2.5 + 12 B = 47 ———-> 5 + 12B = 47 ———> 12B = 42 ——> B = 3.5

So each pound of almonds cost $2.5, and each pound of jelly beans cost $3.5

Answer 2