Question

a store is having a sale on jelly beans and almonds today. the table below shows the amount of each type of food two purchases today.

	amount of jelly beans (in pounds)	amount of almonds (in pounds)	total cost (in dollars)
second purchase	3	5	17

let x be the cost (in dollars) for each pound of jelly beans.
let y be the cost (in dollars) for each pound of almonds.

(a) write a system of equations that could be used to find the cost (in dollars) for each pound of jelly beans and each pound of almonds.
□x + □y = □
□x + □y = □

(b) how much does each pound of jelly beans and each pound of almonds cost (in dollars)?
cost for each pound of jelly beans: $□
cost for each pound of almonds: $□

Explanation:

Part (a)

Step1: Analyze first purchase

The first purchase has 9 pounds of jelly beans (cost \(9x\)) and 7 pounds of almonds (cost \(7y\)), total cost $37. So equation: \(9x + 7y = 37\)

Step2: Analyze second purchase

The second purchase has 3 pounds of jelly beans (cost \(3x\)) and 5 pounds of almonds (cost \(5y\)), total cost $17. So equation: \(3x + 5y = 17\)

Step1: Multiply second equation

Multiply \(3x + 5y = 17\) by 3: \(9x + 15y = 51\)

Step2: Subtract first equation

Subtract \(9x + 7y = 37\) from \(9x + 15y = 51\):
\((9x - 9x) + (15y - 7y) = 51 - 37\)
\(8y = 14\)
\(y = \frac{14}{8} = 1.75\)

Step3: Substitute y into second equation

Substitute \(y = 1.75\) into \(3x + 5y = 17\):
\(3x + 5(1.75) = 17\)
\(3x + 8.75 = 17\)
\(3x = 17 - 8.75 = 8.25\)
\(x = \frac{8.25}{3} = 2.75\)

Answer:

\(9x + 7y = 37\)
\(3x + 5y = 17\)

Part (b)