Intermediate Algebra Answer 2

Intermediate Algebra Answer 2:

2. A company sells jeans and T-shirts. J represents jeans and T represents T-shirts in the equations below:

2J + T = $50
J + 2T = $40

Sarah buys one pair of jeans and one T-shirt. How much does she pay for her entire purchase?

F. $10

G. $20

H. $30

J. $70

K. $90

The correct answer is H.

This type of problem involves knowledge of systems of equations. In other words, you have two equations which both have the same two variables.

In order to solve the problem, take the second equation and isolate J on one side of the equation. By doing this, you define variable J in terms of variable T.

J + 2T = $40
J + 2T - 2T = $40 - 2T
J = $40 - 2T

Now substitute $40 - 2T for variable J in the first equation to solve for variable T.

2J + T = 50
2(40 - 2T) + T = 50
80 - 4T + T = 50
80 - 3T = 50
80 - 3T + 3T = 50 + 3T
80 = 50 + 3T
80 - 50 = 50 - 50 + 3T
30 = 3T
30 ÷ 3 = 3T ÷ 3
10 = T

So now that we know a T-shirt costs $10, we can substitute this value in one of the equations in order to find the value for the jeans, which is variable J.

2J + T = 50
2J + 10 = 50
2J + 10 - 10 = 50 - 10
2J = 40
2J ÷ 2 = 40 ÷ 2
J = 20

Now solve for Sarah's purchase. If she purchased one pair of jeans and one T-shirt, then she paid: $10 + $20 = $30

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