Today in class, Mr. Harbeck taught us how to do a problem solving question. Now, I'm going to scribe how to do/answer a problem solving question using numbers.

**1.** The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.

The numbers are ____and____. **(You can also write this at the end of the equation)**

4x would be on the right side of the + sign, because it is the second number. The first number is x.

So, the equation would be like this:Let x = first #x + 4x = 50

5x = 50 (combined terms)

x = 10

The answer is **10, 40**

You must write the formula x + 4x = 50

10 + 4(10) = 50

10 + 40 = 50

50 = 50

x = 10

4x = 40

**2.** The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers.

The numbers are ____,____,and ____. **(You can also write this at the end of the equation)**

Two other # would equal x because we don't know anything about them.

let x = small # 1 and small # 2

x + 12 + x + x = 84

3x + 12 = 84 (combined terms)

-12 -123x = 72

x= 24

The answer is **36, 24, 24**

**4.** The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.

The numbers are ____,and ____. **(You can also write this at the end of the equation)**

let x = first#

5 more than twice the first

2x + 5

the sum is 80

= 80

x + 2x + 5 = 80

3x + 5 = 80

- 5 -53

x = 75

3x = 25

2x+5 = 55

x = 25

The answer is **25, 55**

**6.** Find two numbers whose sum is 92, if the first is 4 more than 7 times the second. Find the* first* number.

The numbers are ____,and ____. **(You can also write this at the end of the equation)**

let x = second #

(7x + 4) + x = 92

8x + 4 = 92 (combined terms)

- 4 -4

8x = 88

8x = 11

(7x + 4) + x = 92

8(11) + 4 = 92

88 + 4 = 92

92 = 92x

= 117

x + 4 = 81

The answer is **11, 92**

**8.** Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet.

The price is____. **(You can also write this at the end of the equation)**

Let x = bracelet

3x = Necklace

3x + x = 19

24x = 192

4x = $48 ($48.00)

3x = 3

(48)= 144

x = 48

$144.00+$48.00

$192.00

The price of a bracelet is **$48.00** and the necklace is **$144.00.**