Setting Up System of Equation Word Problems

Today, we are going to practice reading a paragraph word problem and writing a System of Equations (2 or more equations) that we will learn to solve the next class period.

The sum of two numbers is 36. Their difference is 6. Find the

numbers.

Identify your variables. First Number = x

Second Number = y

The sum of two numbers is 36. x + y = 36

Their difference is 6. x - y = 6

Now your system is set-up!

The sum of two numbers is 15. Twice one number equals 3 times

the other. Find the numbers.

Identify your variables. First Number = x

Second Number = y

The sum of two numbers is 15. x + y = 15

Twice one number equals 3 times the other. 2x = 3y

Now your system is set-up!

The volleyball club has 41 members. There are 3 more boys than girls. How

many girls are there?

Identify your variables. boys = b

girls = g

The volleyball club has 41 members. b + g = 41

There are 3 more boys than girls. b = g + 3

Now your system is set-up!

A rectangle has a perimeter of 18 cm. Its length is 5 cm greater than

its width. Find the dimensions.

Identify your variables. Length = l

Width = w

A rectangle has a perimeter of 18 cm. 2l + 2w = 18

Its length is 5 cm greater than its width. l = 5 + w

Now your system is set-up!

Timmy has 180 marbles, some plain and some colored. If there are 32 more plain marbles than colored marbles, how many colored

marbles does he have?

Identify your variables. Plain marbles = p

Colored marbles = c

Timmy has 180 marbles. p + c = 180

If there are 32 more plain marbles than colored marbles.

p = c + 32

Now your system is set-up!

A theater sold 900 tickets to a play. Floor seats cost $12 each and balcony seats $10 each.

Total receipts were $9780. How many of each

type of ticket were sold?

Identify your variables. Floor seats = f

Balcony seats = b

A theater sold 900 tickets to a play. f + b = 900

Floor seats cost $12 each and balcony seats $10 each. Total receipts were $9780

12f + 10b = 9780

Now your system is set-up!

TAKS Examples• At a college bookstore, Carla purchased a math textbook and a novel that

cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• F m + n = 8• m = 3n + 54• G m + n = 8• m = 3n - 54• H m + n = 54• m = 3n + 8• J m + n = 54• m = 3n - 8

TAKS Examples• The student council at Jefferson High School sold a total of 220

brownies and cookies during its fund-raiser. Each brownie sold for $0.75, and each cookie sold for $0.50. The student council made $136.50 from the sales of brownies and cookies. Which system of linear equations can be used to find b, the number of brownies sold, and c, the number of cookies sold?

• A b + c = 220• 0.50b + 0.75c = 136.50• B b + c = 136.50• 0.75b + 0.50c = 220• C b + c = 136.50• 0.50b + 0.75c = 220• D b + c = 220• 0.75b + 0.50c = 136.50