Systems of Equations Word Problems Worksheets - Math Monks - Free Printable

Let's solve each of these systems of two equations word problems step by step.

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Problem 1: Nancy’s Shirts

> Nancy spent $140 on shirts. Fancy shirts cost $20 and plain shirts cost $15. If she bought 8 shirts in total, then how many of each kind did she buy?

#### Step 1: Define variables
Let:
- $ f $ = number of fancy shirts
- $ p $ = number of plain shirts

#### Step 2: Set up equations
1. Total number of shirts:
$ f + p = 8 $

2. Total cost:
$ 20f + 15p = 140 $

#### Step 3: Solve the system

From equation (1):
$ f = 8 - p $

Substitute into equation (2):
$ 20(8 - p) + 15p = 140 $
$ 160 - 20p + 15p = 140 $
$ 160 - 5p = 140 $
$ -5p = -20 $
$ p = 4 $

Then $ f = 8 - 4 = 4 $

✔ Answer: Nancy bought 4 fancy shirts and 4 plain shirts.

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Problem 2: Noah’s Investment

> Noah invests a total of $20,000 in two accounts, one paying 5% and the other paying 8% simple interest per year. Her annual interest is $1,180. How much did she invest at each rate?

#### Step 1: Define variables
Let:
- $ x $ = amount invested at 5%
- $ y $ = amount invested at 8%

#### Step 2: Set up equations
1. Total investment:
$ x + y = 20,000 $

2. Total interest:
$ 0.05x + 0.08y = 1,180 $

#### Step 3: Solve the system

From equation (1):
$ x = 20,000 - y $

Substitute into equation (2):
$ 0.05(20,000 - y) + 0.08y = 1,180 $
$ 1,000 - 0.05y + 0.08y = 1,180 $
$ 1,000 + 0.03y = 1,180 $
$ 0.03y = 180 $
$ y = \frac{180}{0.03} = 6,000 $

Then $ x = 20,000 - 6,000 = 14,000 $

✔ Answer:
- $14,000 invested at 5%
- $6,000 invested at 8%

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Problem 3: Two Numbers

> Two times a number added to another number is 25. Three times the first number minus the other number is 20. Find the two numbers.

#### Step 1: Define variables
Let:
- $ x $ = first number
- $ y $ = second number

#### Step 2: Set up equations
1. $ 2x + y = 25 $
2. $ 3x - y = 20 $

#### Step 3: Solve the system

Add equations (1) and (2) to eliminate $ y $:
$ (2x + y) + (3x - y) = 25 + 20 $
$ 5x = 45 $
$ x = 9 $

Substitute $ x = 9 $ into equation (1):
$ 2(9) + y = 25 $
$ 18 + y = 25 $
$ y = 7 $

✔ Answer: The two numbers are 9 and 7.

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Problem 4: Chickens and Pigs

> There are 13 animals in a barn. Some are chickens and some are pigs. There are 40 legs in all. Find the number of each animal.

#### Step 1: Define variables
Let:
- $ c $ = number of chickens (2 legs each)
- $ p $ = number of pigs (4 legs each)

#### Step 2: Set up equations
1. Total animals:
$ c + p = 13 $

2. Total legs:
$ 2c + 4p = 40 $

#### Step 3: Solve the system

From equation (1):
$ c = 13 - p $

Substitute into equation (2):
$ 2(13 - p) + 4p = 40 $
$ 26 - 2p + 4p = 40 $
$ 26 + 2p = 40 $
$ 2p = 14 $
$ p = 7 $

Then $ c = 13 - 7 = 6 $

✔ Answer:
- 6 chickens
- 7 pigs

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✔ Final Answers Summary:

1. Fancy shirts: 4, Plain shirts: 4
2. 5% account: $14,000, 8% account: $6,000
3. Two numbers: 9 and 7
4. Chickens: 6, Pigs: 7

Let me know if you'd like these solutions shown with graphs or tables!