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MPM 1D Lesson E5 - Solving Equations Word Problems and Applications
Date:_____________
Part A – length and width types
1) The length of a rectangle is 3 times the width. The perimeter is 96cm. Find the width and the length.
2) The length of a rectangle is 5m greater than the width. The perimeter is 150m. Find the width and the
length.
3) The width of a rectangle is 12cm less than the length. The perimeter is 156cm. Find the width and the
length.
4) The length of a rectangle is 2 cm less than 7 times the width. The Perimeter is 60cm. Find the width
and the length.
5) The perimeter of a triangle is 76cm. Side ‘a’ of the triangle is twice as long as side ‘b’. Side ‘c’ is 1
cm longer than side ‘a’. Find the length of each side.
6) The first side of a triangle is 8m shorter than the second side. The third side is 4 times as long as the
first side. The perimeter is 26m. Find the length of each side.
7) A triangular sail has a perimeter of 25m. Side ‘a’ is 2m shorter than side ‘b’ and side ‘c’ is 3m longer
than side ‘b’. Find the length of each side.
8) A isosceles triangle with perimeter of 570m has an unequal side that is 30m shorter than twice the
length of each congruent side. Find the length of each side.
Answers:
1. 12 and 36
5. 15, 30 and 31
2. 35 and 40
6. 3, 11 and 12
3. 33 and 45
7. 6 , 8 and 11
4. 4 and 26
8. 150, 150 and 270
Part B – Numbers Types
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The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.
The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers.
The sum of two numbers is 45. The first is 9 less than the second. Find the numbers.
The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.
The larger of two numbers is 1 less than 3 times the smaller. Their sum is 63. Find the numbers.
Find the two numbers whose sum is 92, if the first is 4 more than 7 times the second.
The sum of two numbers is 172. The first is 8 less than 5 times the second. Find the first number.
Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as
much as the bracelet.
9) Grandpa’s age is 6 years less than 6 times Matt’s age. The sum of their age is 78. Find each of their
ages.
10) The first of two films lasted 3 minutes less than twice as long as the second. Together the two films
lasted 132 minutes. How long was the first film?
Answers:
1. 10, 40
5. 16, 47
9. 66, 12
2. 36, 48
6. 11, 81
10. 87 mins.
3. 18, 27
7. 30, 142
4. 25, 55
8, $48, $144
Part C – Numbers and Age Types
1) A tree trunk is 15m long is cut into 2 pieces. One piece is 4 times as long as the other. How long is
each piece?
2) Find 2 consecutive numbers whose sum is 263.
3) One number is 5 times another number. If the 2 numbers total 18, find the numbers.
4) Sasha is three years older than Rumya; the sum of their ages is 35. How old is Rumya?
5) For two consecutive integers, the sum of the smaller and twice the larger is 38. What are the
integers?
Answers:
1) 3,12
2) 131, 132
3) 3, 15
4) 16
5) 12, 13
Part D – Money Types
1) Kajal has nickels and dimes worth $0.85. She has 2 more nickels than dimes. How many
nickels and dimes does she have?
2) A jar contains $18.50 in dimes and quarters. There are 110 coins in the jar. How many
quarters are in the jar?
3) The cost of a pen is 3 times the cost of a pencil. The cost of 4 pencils and 3 pens is $9.75.
What is the cost of a pencil?
4) A service station has 22 mufflers in stock, worth a total of $422. The premium mufflers are
worth $23 each and is $7 more than the standard mufflers. How many premium mufflers
are in stock?
5) A vending machine contains nickels, quarters, and dimes with a total value of $83.75. Three are
twice as many dimes as nickels, and 50 more quarters than dimes. How many of each coin are in
the machine?
6) Tickets to the concert cost $9 for adults and $6.50 for students. A total of 950 people paid $7675 to
attend. How many students attended the concert?
7) A pile of nickels and dimes has a value of $4.50. There are three times as many nickels as dimes.
How many nickels and how many dimes are there?
8) A parking meter accepts only quarters and dollars. If there are 31 coins with a value of $20.50, how
many quarters and how many dollars are there?
9) Ahmed sells tickets at the theatre. At the end of the evening, he had $524.00 in $2 and $5 bills.
The total number of bills was 145. How many of each kind of bill were there in total?
10) One of the equal sides of an isosceles triangle is 3m less than twice its base. The perimeter is 44m.
Find the lengths of the sides.
11) Laibah has twice as many dimes as nickels. The total value is $3.50. How many nickels does she
have?
Answers:
1) 5, 7
7) 18, 54
2) 60, 50
8) 14, 17
3) 0.75, 2.25
9) 67, 78
4) 10
5) 95, 190, 240
6) 350
10) 17, 17, 10
11) 14, 28
Part E – Mix Types - Solving Equations Word Problems
Date:_____________
1) Seven times a number is the same as twenty-four more tan three times the number. Find the number.
2) Seven more than three times a number is the same as five less than nine times a number. Find the
number.
3) One number is 5 times another number. The sum of the two numbers is 132. Find the two numbers.
4) Find two consecutive numbers with a sum of 149.
5) Find two consecutive odd numbers whose sum is 48.
6) Find more than 7 times a number is the same as twenty more than twice the number. Find the number.
7) Nine times a number minus two times the number is the same as thirty-two less than three times the
number. Find the number.
8) The sum of two numbers is 34. The difference between the two numbers is 4. Find the two numbers.
9) The length of a rectangle is x+5 cm and the width is x cm. If the perimeter is 74 cm, write an
equation. Find the dimensions of the rectangle.
10) A rectangle with sides 2a+5 and a+3 has a perimeter of 148 cm. Find the length and the width of the
rectangle.
11) The length of a rectangle is 3 cm less than five times the width. The perimeter is 90 cm. Find the
width and the length of the rectangle.
12) The sides of a triangle are given by the expressions y, y+5, and y+8 cm. If the perimeter of the
triangle is 49, what are the lengths of each side of this triangle?
13) The length of a rectangle is fours times the width. If the length is decreased by 12m and the width
increased by 12m, the rectangle becomes a square. Find the dimensions of the original rectangle.
14) A banquet hall charges $500 to rent the hall and $30 per person for a meal.
a. If 200 people attend the banquet how much money will it cost to host the event?
b. If the budget for the event is $15500, how many people can attend?
Answers: to be taken up.
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2)
7)
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14) a.
b.
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