Respuesta :
the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75
Step-by-step explanation:
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.
⇒ [tex]3x+2y=11[/tex] → (1)
For 5 pounds of jelly beans and 6 pounds of trail mix, the total cost is $23
⇒ [tex]5x+6y=23[/tex] → (2)
Solving (1) and (2), we get
3(1 equation)-(2 equation)=0
⇒[tex]3(3x+2y)-5x-6y=3(11)-23[/tex]
⇒[tex]9x+6y-5x-6y=10[/tex]
hence,
⇒[tex]4x=10[/tex]
⇒[tex]x=2.5[/tex]
Putting [tex]x=2.5[/tex] in [tex]3x+2y=11[/tex] we get ;
⇒ [tex]3x+2y=11[/tex]
⇒ [tex]3(2.5)+2y=11[/tex]
⇒ [tex]2y=11-7.5=3.5[/tex]
⇒ [tex]y=1.75[/tex]
Hence, the cost for each of jelly beans and each pound of trail mix is $2.5 and $1.75 .
