### Practical Calculations on the Exam

Many of the questions on the math section of the ACT will ask you to do practical calculations.

For instance, you may be asked to calculate the dimensions of an object or the price of an item in a store after a discount is given.

Other common practical calculations might involve computations with exam scores or other data for a class of students.

### Practical Calculations – Sample Problem

Now have a look at another type of practical calculation, which involves knowledge of systems of equations.

A company sells jeans and T-shirts.

*J*represents jeans and

*T*represents T-shirts in the equations below:

2*J* + *T* = $50

*J* + 2*T* = $40

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

A. $10

B. $20

C. $30

D. $70

E. $90

**The correct answer is C.**

For systems of equations problems, you will see two equations which both have the same two variables, like *J* and *T* in the problem above.

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* + 2*T* = $40

*J* + 2*T* − 2*T* = $40 − 2*T*

*J* = $40 − 2*T*

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

2*J* + *T* = 50

2(40 − 2*T*) + *T* = 50

80 − 4*T* + *T* = 50

80 − 3*T* = 50

80 − 3*T* + 3*T* = 50 + 3*T*

80 = 50 + 3*T*

80 − 50 = 50 − 50 + 3*T*

30 = 3*T*

30 ÷ 3 = 3*T* ÷ 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*.

2*J* + *T* = 50

2*J* + 10 = 50

2*J* + 10 − 10 = 50 − 10

2*J* = 40

2*J* ÷ 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