1.) **First odd integer: x**

Second odd integer: x + 2

Equation:

5x + 3(x+2) = 62

5x + 3x + 6 = 62

8x = 62 - 6

8x = 56

8x/8 = 56/8

x = 7

**ANSWER: The first odd integer is 7.**

The second odd integer is:

x + 2 = (7) + 2 = **9**

Check:

5 (7) + 3 (9) = 62

35 + 3(9) = 62

35 + 27 = 62

62 = 62

2) Present ages:

Carol's brother: x

Carol: 5x

Ages in two years:

Carol's brother: x + 2

Carol: 5x + 2

Equation:

5x + 2 = 3(x + 2)

5x + 2 = 3x + 6

5x - 3x = 6 - 2

2x = 4

2x/2 = 4/2

**x = 2**

**Present ages: **(Substitute 2 for x)

**Carol's brother**: x = **2 years old**

**Carol:** 5x = 5(2) = **10 years old**

**ANSWER: Carol is now 10 years old.**

Ages in 2 years:

Carol's brother: 2 + 2 = 4 years old

Carol: 10 + 2 = 12 years old

In two years, Carol will be three times as old as her brother.

12 = 3 (4)

12 = 12