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?
A 28 pounds
B 29 pounds
C 30 pounds
D 58 pounds

Answer:

B

Step-by-step explanation:

oranges weigh 0.5 and grapefruits weigh 1.5

The required: 13 oranges and 15 grapefruits would weigh 29 pounds.

The correct option is A.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Let's use a system of equations to solve this problem:

Let's call the weight of an orange "x" and the weight of a grapefruit "y". Then we can write:

10x + 20y = 35 (equation 1)

16x + 10y = 23 (equation 2)

We want to find the weight of 13 oranges and 15 grapefruits, which we can represent as:

13x + 15y

In this case, we can multiply equation 1 by -8 and equation 2 by 15:

-80x - 160y = -280 (equation 1, multiplied by -8)

240x + 150y = 345 (equation 2, multiplied by 15)

Now we can add the two equations to eliminate y:

160x = 65

Solving for x, we get:

x = 65/160

Now we can substitute this value of x back into one of the original equations to solve for y. Let's use equation 1:

10(65/160) + 20y = 35

Simplifying this equation, we get:

13/32 + 2y/4 = 7/2

Multiplying both sides by 32, we get:

13 + 16y = 112

Solving for y, we get:

y = 99/16

Finally, we can substitute these values of x and y into the expression for 13 oranges and 15 grapefruits:

13x + 15y = 13(65/160) + 15(99/16) = 29.0625

Therefore, 13 oranges and 15 grapefruits would weigh approximately 29.0625 pounds, which is closest to answer B, 29 pounds.

To learn more about the system of equations;

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