Question

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 34 dollars. For 5 pounds of almonds and 2 pounds of jelly beans. the cost is 17 dollars. Find the cost of each pound of almonds and each pound of jelly beans

Answer 1

We have a system of equation problem

x= cost of almonds per pound

y= cost of the jelly beans per pound

For the first equation, we have

3 pounds of almonds

8 pounds of jelly beans

total $34

so the equation is

3x+8y=34

For the second equation we have

5 pounds of almonds

2 pounds of jelly beans

total $17

so the equation is

5x+2y=17

so our system of equation is

`\begin{gathered} 3x+8y=34 \\ 5x+2y=17 \end{gathered}`

In order to solve the system we will multiply the second equation by -4

`-4(5x+2y=17)=-20x-8y=-68`

then we sum the equation above with the first equation

`3x-20x+8y-8y=34-68`

then we sum similar terms and isolate the x to find the value of x

`\begin{gathered} -17x=-34 \\ x=(-34)/(-17) \\ x=2 \end{gathered}`

then we substitute the value of x=2 in the first equation and we find the value of y

`\begin{gathered} 3(2)+8y=34 \\ 6+8y=34 \\ 8y=34-6 \\ 8y=28 \\ y=(28)/(8) \\ y=3.5 \end{gathered}`

The solution is

x= $ 2 cost of each pound of almond

y= $3.50 cost of each pound of jelly beans