Question

Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y.

750x + 17y = 141.61
300x + 30y = 75.90
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?

a. The cost of electricity is $0.17 per unit.
b. The cost of natural gas is $0.20 per unit.
c. The cost of electricity is $0.72 per unit.
d. The cost of natural gas is $0.83 per unit.

Answer 1

D: The cost of natural gas is $0.83 per unit.

Answer 2

Option d is correct

The cost of natural gas (y) = $0.83 per unit

Explanation:

Given the system of equation:

750x + 17y = 141.61 ......[1]

300x + 30y =75.90 ......[2]

where x is the cost of electricity and y is the costs of natural gas.

Multiply equation [1] by 30 and equation [2] by 75 we get;

`30 \cdot (750x + 17y) = 30 \cdot 141.61`

Simplify:

22500x + 510y = 4248.3 ......[3]

`75 \cdot (300x + 30y) = 75 \cdot 75.90`

Simplify:

22500x + 2250y = 5692.5 .......[4]

Subtract equation [3] from [4] we get;

1740 y = 1444.2

Divide by 15 both sides, we get

116 y = 96.28

Since, Katrina solves the above system using linear equation and arrives at the equation :

116 y = 96.28

Division property of equality states that divide the same number to both sides of an equation:

Divide by 116 to both sides of an equation, to solve for y;

`(116 y)/(116) =(96.28)/(116)`

Simplify:

y = 0.83 where y represents the cost of natural gas

Therefore, the cost of natural gas y ,is, $ 0.83 per unit.