Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 8 small boxes has a total weight of 106 kilograms. A delivery of 5 large boxes and 2 small boxes has a total weight of 103 kilograms. How much does each type of box weigh?

Answer 1

We will call small boxes x and big boxes y. This will mean that we have 2 different equations using the same two unknown weights. So, 2×y+8×x=106 and 5×y+2×x=103. Find how x and y relate to each other and apply it to one any of the equtions. 5y+2x=103 is the same as 5y=103-2x, and same as y=(103-2x)/5. Apply this relation we found to the other equation and we can find 2((103-2x)÷5)+8x=106, to (206-4x)÷5+8x=106, to (206+36x)÷5=106, to 206+36x=530, to 36x=324, to x=9. Apply again to any equation to find y, 5y+2(9)=103. 5y+18=103, to 5y=85, so y=17. Small boxes are 9kg and large boxes are 17kg