Question

10 oranges and 20 grapefruits weigh 35 pounds total. 16 oranges and 10grapefruits weigh 23 pounds total. How much would 13 oranges and 15grapefruits weigh?A 28 poundsB 29 poundsC 30 poundsD 58 pounds20 Illuminate Education, Inc.

Answer 1

First, we will find the weight of each oranges and grape fruit

Let x be the unit weight of orange

Let y be the unit weight of grape fruit

If "10 oranges and 20 grapefruits weigh 35 pounds total"

Then this implies;

10x + 20 y = 35 -----------------(1)

And

If " 16 oranges and 10 grapefruits weigh 23 pounds total"

This implies;

16x + 10y = 23 ---------------------(2)

We can solve the two equations simultaneously.

Using elimination method;

we eliminate y and to do that, the y variables in the two equations must be same, Hence we can achieve that by multiply equation (1) by 10 and then multiply equation (2) by 20

100x + 200y = 350 ----------------------------(3)

320x + 200y = 460 ------------------------------(4)

subtract equation (3) from equation (4)

220x = 110

divide both-side of the equation by 220

x = 0.5

substitute x=0.5 into equation(1) and then solve for y

10(0.5) + 20y = 35

5 + 20y = 35

subtract 20 from both-side of the equation

20y = 35 - 5

20y = 30

divide both-side of the equation by 20

y = 1.5

"13 oranges and 15 grape fruits" = 13 x + 15y

substituting x = 0.5 and y= 1.5 in the above;

13(0.5) + 15(1.5)

=6.5 + 22.5

=29

Hence;

13 oranges and 15 grapefruits will weigh 29 pounds