### All ACT Math Resources

## Example Questions

### Example Question #5 : Rational Expressions

Find the product of and .

**Possible Answers:**

**Correct answer:**

Solve the first equation for .

Solve the second equation for .

The final step is to multiply and .

### Example Question #1 : Rational Expressions

The following table shows the temperature of a cup of coffee at different times

Time 1:09 1:11 1:13 1:15 1:17

Temperature (ºF) 187.1 184.4 181.7 179.0 176.3

If this trend continues, what will the temperature of the coffee at minute 1:25?

**Possible Answers:**

168.3°F

165.5°F

160.2°F

171.0°F

162.9°F

**Correct answer:**

165.5°F

The table shows that for every two minutes, the temperature of the coffee lowers 2.7ºF. At 1:25, 16 minutes, or eight 2-minute intervals have passed, and the temperature of the coffee has lowered by 8*2.7ºF, reaching a temperature of 165.5ºF.

### Example Question #7 : Rational Expressions

Amy buys concert tickets for herself and her friends. She initially buys them at $40/ticket. Weeks later, her other friends ask her to buy them tickets, but the prices have increased to $54. Amy buys 7 tickets total and spends $350. How many tickets has she paid $40 on?

**Possible Answers:**

**Correct answer:**

Amy has bought 7 tickets, x of them at $40/ticket, and the remaining 7-x at $54/ticket. She spends at total of

### Example Question #8 : Rational Expressions

What is

?

**Possible Answers:**

**Correct answer:**

To find an equivalency we must rationalize the denominator.

To rationalize the denominator multiply the numerator and denominator by the denominator.

To simplify completely, factor out a three from the numerator and denominator resulting in the final solution.