1. (a) x + 5 = 9
(b) x - 3 = 12
(c) 5x - 2 = 4
(d) 2(x + 7) = 13
2. Let the smaller number be x. Then the larger number is x + 12.
x + (x + 12) = 48
2x + 12 = 48
2x = 36
x = 18
The numbers are 18 and 30.
3. Let the number be x.
2x - 22 = 48
2x = 70
x = 35
4. Let the number be x.
7x = 10x - 36
36 = 3x
x = 12
5. Let the number be x.
(4/5)x = (3/4)x + 5
Multiply both sides by 20: 16x = 15x + 100
x = 100
6. Let the first even number be x. Then the next consecutive even number is x + 2.
x + (x + 2) = 38
2x + 2 = 38
2x = 36
x = 18
The numbers are 18 and 20.
7. Let the first odd number be x. Then the next two consecutive odd numbers are x + 2 and x + 4.
x + (x + 2) + (x + 4) = 51
3x + 6 = 51
3x = 45
x = 15
The numbers are 15, 17, and 19.
8. Let Rene's current age be x. Then her sister's current age is x - 6.
In 10 years: (x + 10) + ((x - 6) + 10) = 50
2x + 14 = 50
2x = 36
x = 18
Rene is 18 years old, and her sister is 12 years old.
9. Let the breadth be x meters. Then the length is x + 10 meters.
Perimeter = 2(length + breadth) = 80
2((x + 10) + x) = 80
2(2x + 10) = 80
4x + 20 = 80
4x = 60
x = 15
The breadth is 15 m, and the length is 25 m.
10. Let the width be x meters. Then the length is 2x meters.
Perimeter = 2(length + width) = 300
2(2x + x) = 300
2(3x) = 300
6x = 300
x = 50
The width is 50 m, and the length is 100 m.
11. Let the numerator be x. Then the denominator is x + 8.
(x + 17) / ((x + 8) - 1) = 3/2
(x + 17) / (x + 7) = 3/2
Cross-multiply: 2(x + 17) = 3(x + 7)
2x + 34 = 3x + 21
34 - 21 = 3x - 2x
13 = x
The fraction is 13/21.
Parent Tip: Review the logic above to help your child master the concept of linear equation word problems worksheet with answers.
