Question

-8-7.10 oranges and 20 grapefruits weigh 35 pounds total. 16 oranges and 10 grapefruits weigh 23 pounds total. How much would 13 oranges and 15 grapefruits weigh?

Answer 1

10 oranges + 20 grapefruits = 35 pounds

16 oranges + 10 grapefruits = 23 pounds

13 oranges + 15 grapefruits = ?

Let x represent one orange and y represent one grapefruit, you can express the given equivalencies as equations:

10 oranges + 20 grapefruits = 35 pounds → 10x+20y=35

16 oranges + 10 grapefruits = 23 pounds→ 16x+10y=23

13 oranges + 15 grapefruits = ? → 13x+15y= ?

With this, we determined an equation system with two unknowns.

Write the first equation in terms of y:

Next is to replace it in the second equation:

`\begin{gathered} 16x+10y=23 \\ 16x+10((7)/(4)-(1)/(2)x)=23 \\ 10x+10\cdot(7)/(4)+10\cdot(-(1)/(2)x)=23 \\ 10x+(35)/(2)-5x=23 \\ 10x-5x=23-(35)/(2) \\ 5x=(11)/(2) \\ x=(11)/(10) \end{gathered}`

Third step is to calculate the value of y

`\begin{gathered} y=(7)/(4)-(1)/(2)x \\ y=(7)/(4)-(1)/(2)\cdot(11)/(10) \\ y=(6)/(5) \end{gathered}`

Finally, now that you know the values of x and y you can replace the third formula and calculate:

`\begin{gathered} 13x+15y=\text{?} \\ 13\cdot(11)/(10)+15\cdot(6)/(5)=(323)/(10)=32.3 \end{gathered}`

13 oranges and 15 grapefruits will weight 32.3 pounds