SUBSTITUTION METHOD WORD PROBLEMS WORKSHEET

Problem 1 :

Two numbers have a sum of 200 and a difference of 37. Find the numbers.

Solution

Problem 2 :

The difference between two numbers is 84 and their sum is 278. What is the numbers?

Solution

Problem 3 :

One number exceeds another by 11. The sum of the two numbers is 5. What are the numbers?

Solution

Problem 4 :

The larger of two numbers is four times the smaller and their sum is 85. Find the two numbers.

Solution

Problem 5 :

A wedding planner purchased both small and large lanterns for a wedding reception. The planner purchased a total of 40 lanterns for a purchase price of $1180. How many of each size lantern did the planner purchase?

Solution

write an equation that represents the sum of the angle measures of the parallelogram and (b) use your equation and the equation shown to find the values of x and y.

Problem 6 :

Solution

Problem 7 :

Solution

Problem 1 :

Find two integers such that three times the smaller is 33 more than twice the larger and twice the smaller plus five times the larger equals 250.

Solution

Problem 2 :

Two hammers and a screwdriver cost a total of $34. A hammer and 3 screwdrivers cost a total of $32. Find the price of each type of tool.

Solution

Problem 3 :

Four adults and three children go to a theatre for $74, where as two adults and five children are charged $58. Find the price of an adult’s ticket and a child’s ticket.

Solution

Problem 4 :

Three blankets and a sheet cost me $190. Two sheets and a blanket cost a total of $100. Find the cost of one blanket and one sheet.

Solution

Problem 5 :

Seven peaches plus eight nashi cost me $273 altogether. However, three peaches and one nashi cost a total of $66. Find the cost of one piece of each fruit.

Solution

Problem 6 :

A purse contains $3.75 in 5 cent and 20 cent coins. If there are 33 coins altogether, how many of each type of coin are in the purse?

Solution

Problem 7 :

Asha is five years older than Robert. Five years ago, Asha was twice as old as Robert was then. Find their present ages.

Solution

Problem 1 :

y = -3x + 4

y = 4x - 10

Solution

Problem 2 :

y = -4x + 2

y = 6x - 8

Solution

Problem 3 :

x = - 2y

x - y = 9

Solution

Problem 4 :

y = 2x

-6x + 3y = 16

Solution

Problem 5 :

y = -3x

4x - 2y = -20

Solution

Problem 6 :

y = 3x - 4

4x + 3y = 1

Solution

Problem 7 :

y = x - 4

-4x - 6y = -16

Solution

Problem 8 :

x = 3y + 1

2x + 4y = 12

Solution

Problem 9 :

x = y - 4

-2x + 3y = 6

Solution

Problem 10 :

Next week your math teacher is giving a chapter test. The test will consist of 35 questions. Some problems are worth 2 points and some problems are worth 4 points. There are 20 questions worth 2 points. How many problems of 4 points are on the test?

Solution

Use the method of substitution to solve:

Problem 1 :

x = 1 + 2y

2x + y = 17

Solution

Problem  2 :

y + 4x = 6

y = 2x + 3

Solution

Problem 3 :

x = 2y - 6

2x + y = 8

Solution

Problem 4 :

3x - 2y = 5

y = 3 - 4x

Solution

Problem 5 :

x = 1 - 2y

3x + y = 13

Solution

Problem 6 :

x = 3y + 12

3x - 2y = 8

Solution

Problem 7 :

y = 3x - 2

2x - 5y = 27

Solution

Problem 8 :

x = 4y - 1

3x + 4y = -1

Solution

Problem 9 :

y = 5x + 7

2x - 3y = 8

Solution