Answer:
Cost of 1 case of oranges is $ 15 and cost of 1 case of grapefruits is $ 20
(Cost of 1 case of oranges and 1 case of grapefruits altogether equal to [tex]15+20=\$35[/tex])
Step-by-step explanation:
Let cost of 1 case of oranges be [tex]\$x[/tex] and cost of 1 case of grapefruits be [tex]\$y[/tex]
As cost of 5 cases of oranges and 8 cases of grapefruit is $235,
[tex]5x+8y=235[/tex] ...(i)
As cost of 3 cases of oranges and 2 cases of grapefruit is $85,
[tex]3x+2y=85[/tex] ...(ii)
Multiply equation (ii) by [tex]-4[/tex]
[tex]-12x-8y=-340[/tex] ...(iii)
Add (i) and (iii)
[tex]-7x=235-340\\-7x=-105\\x=\frac{-105}{-7}\\ =15[/tex]
Put [tex]x=15[/tex] in (i)
[tex]5(15)+8y=235\\75+8y=235\\8y=235-75\\8y=160\\y=\frac{160}{8}=20[/tex]
So,
Cost of 1 case of oranges is $ 15 and cost of 1 case of grapefruits is $ 20
Therefore,
Cost of 1 case of oranges and 1 case of grapefruits altogether equal to [tex]15+20=\$35[/tex]
