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2 pounds almonds and 5 pounds jelly beans total cost $13. 8 pounds almonds and 3 pounds jelly beans total cost $18. What is cost for each pound almonds and each pound jelly beans

User Derrylwc
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1 Answer

5 votes

Answer:

almonds cost $1.50 per pound

jelly beans cost $2 per pound

Explanation:

This is a "system of equations" problem. We need to write out 2 equations, and then use one to solve the other.

They tell us all the numbers we'll need to know.

Let's let:

  • a = the cost of a pound of almonds
  • j = the cost of a pound of jelly beans
  • both in $ per pound of course

From the first sentence they gave us:

2a + 5j = 13

Do you see why that is? 2 pounds of almonds times their cost per pound, and/+ 5 pounds of jelly beans times their cost per pound, would total $13. Good with that?

Then do it for the second sentence:

8a + 3j = 18

Now choose either equation and solve it for either variable. Mathematically it doesn't matter which equation or which variable you choose.

The first equation, solving for a, might be just a tad less complicated, so let's use it. All the steps in case you can't quickly do it:

  • 2a + 5j = 13
  • 2a = -5j + 13
  • a = -2.5j + 6.5

Did you follow all that? I could've used fractions, but it's clearer when typing to use decimals.

Now we have an expression for a in terms of j. That's super-important to understand.

It means we can plug that expression for 'a' into the second equation and find what j is. Watch:

8a + 3j = 18

We now know from the other equation that the relationship between a and j is: a = 2.5j + 6.5. So substitute that in for 'a':

8(-2.5j + 6.5) + 3j = 18

See how the expression for a replaced a? That's very powerful. Now multiply it out:

-20j + 52 + 3j = 18

Now group like terms:

(-20j + 3j) = (18 - 52)

-17j = -34

j = 2

Now we're close, but don't get in a hurry and get tripped up.

What did the variable j represent? The price of jelly beans, and now we know that's $2 per pound.

And remember how we found an expression for a in terms of j? That was a = -2.5j + 6.5. We know j now, so plug it in:

a = -2.5(2) + 6.5 = -5 + 6.5 = 1.50 per pound <-- the price of almonds

You should check those numbers in one or both equations to check your work. I.e., is what you found really true?

User Jon Calder
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