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2 years ago

A. Sarah Smartshopper receives ten cents off per gallon on gas for every $100 she

Mathematics

1 answer:

Wewaii [24]2 years ago

8 0

Using proportions, it is found that her discount is of $0.29664.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount.

In this problem, the total amount she spent on gas is given by:

T = $45.23 + $102.34 + $13.67 + $34.56 + $48.72 + $52.12 = $296.64.

Considering that she receives ten cents off per gallon on gas for every $100 she spends, we apply the <em>proportion </em>to find that her discount is given by:

$D = 0.1 \times \frac{296.64}{100} = 0.29664$

Her discount is of $0.29664.

More can be learned about proportions at brainly.com/question/24372153

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Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2

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Answer:

substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

x = 6y -8

7(6y -8) -y = -2 . . . . . x variable eliminated

The second equation is easily solved for y, so you could substitute that into the first equation.

y = 7x +2

-x +6(7x +2) = 8 . . . . . y-variable eliminated

The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

7(-x +6y) +(7x -y) = 7(8) +(-2)

42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

(-x +6y) +6(7x -y) = (8) +6(-2)

-x +42x = -4 . . . . . . . . y-variable eliminated

It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).

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