Question

PLS HELP ILL MARK BRAINLIEST

A store is having a sale on almonds and jelly beans. For 3 pounds of almonds and 8 pounds of jelly beans, the total cost is $23.
For 5 pounds of almonds and 2 pounds of jelly beans, the total cost is $10. Find the cost for each pound of almonds and each
pound of jelly beans.

Answer 1

Answers:

• one pound of almonds = $1
• one pound of jelly beans = $2.50

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Explanation:

• x = cost of one pound of almonds
• y = cost of one pound of jelly beans

The sentence "For 3 pounds of almonds and 8 pounds of jelly beans, the total cost is $23" tells us we have the equation 3x+8y = 23.

• 3x = cost of just the almonds (3 pounds)
• 8y = cost of just the jelly beans (8 pounds)
• 3x+8y = cost of both items = 23 dollars

So that's how we form the equation 3x+8y = 23.

The next sentence leads to the equation 5x+2y = 10 for similar reasoning.

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The system of equations we have is

$\begin{cases}3x+8y = 23\\5x+2y = 10\end{cases}$

Let's solve for y in the second equation

$5x+2y = 10\\2y = -5x+10\\y = (-5x+10)/2\\y = (-5x)/2+10/2\\y = -2.5x+5$

Then plug this into the first equation and solve for x.

$3x+8y = 23\\3x+8(-2.5x+5) = 23\\3x-20x+40 = 23\\-17x+40 = 23\\-17x = 23-40\\-17x = -17\\x = -17/(-17)\\x = 1$

This tells us that one pound of almonds cost $1

Use this x value in any equation involving x & y to solve for y.

I'll use the equation in which we solved for y.

$y = -2.5x+5\\y = -2.5(1)+5\\y = -2.5+5\\y = 2.5$

Therefore, one pound of jelly beans costs $2.50