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?