the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75
<u>Step-by-step explanation:</u>
Given A store is having a sale on jelly beans and trail mix. For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11. For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23 . We have to find the cost for each pound of trail mix and each pound of jelly beans.
Let the cost of each pound of trail mix is $y.
and the cost of each pound of jelly beans is $x.
According to question,
For 3 pounds of jelly beans and 2 pounds of trail mix, the total cost is $11.
⇒
→ (1)
For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23
⇒
→ (2)
Solving (1) and (2), we get
3(1 equation)-(2 equation)=0
⇒![3(3x+2y)-5x-6y=3(11)-23](https://tex.z-dn.net/?f=3%283x%2B2y%29-5x-6y%3D3%2811%29-23)
⇒![9x+6y-5x-6y=10](https://tex.z-dn.net/?f=9x%2B6y-5x-6y%3D10)
hence,
⇒![4x=10](https://tex.z-dn.net/?f=4x%3D10)
⇒![x=2.5](https://tex.z-dn.net/?f=x%3D2.5)
Putting
in
we get ;
⇒
⇒ ![3(2.5)+2y=11](https://tex.z-dn.net/?f=3%282.5%29%2B2y%3D11)
⇒ ![2y=11-7.5=3.5](https://tex.z-dn.net/?f=2y%3D11-7.5%3D3.5)
⇒ ![y=1.75](https://tex.z-dn.net/?f=y%3D1.75)
Hence, the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75 .