Linear Equation Word Problems worksheet - Free Printable

I'll solve each problem step by step.

Question 1: Solve the linear equations

A) 8x + 3 = 27 + 2x
- Subtract 2x from both sides: 6x + 3 = 27
- Subtract 3 from both sides: 6x = 24
- Divide by 6: x = 4

B) 7y/5 = y - 4
- Multiply both sides by 5: 7y = 5(y - 4)
- Expand: 7y = 5y - 20
- Subtract 5y from both sides: 2y = -20
- Divide by 2: y = -10

Question 2: Two numbers with ratio 3:5

Let the two numbers be 3x and 5x (since their ratio is 3:5).

When each is increased by 10, they become (3x + 10) and (5x + 10).
The new ratio is 5:7.

So: (3x + 10)/(5x + 10) = 5/7

Cross-multiply: 7(3x + 10) = 5(5x + 10)
21x + 70 = 25x + 50
70 - 50 = 25x - 21x
20 = 4x
x = 5

Original numbers: 3x = 15 and 5x = 25

Check: Original ratio = 15:25 = 3:5 ✓
After adding 10: 25:35 = 5:7 ✓

Question 3: Herd of deer

Let the total number of deer be x.

- Half are grazing: x/2
- Remaining: x/2
- Three-fourths of remaining are playing: (3/4)(x/2) = 3x/8
- The rest (9) are drinking

So: x/2 + 3x/8 + 9 = x

Multiply by 8: 4x + 3x + 72 = 8x
7x + 72 = 8x
72 = x

Total deer = 72

Check: Grazing = 36, Playing = 27, Drinking = 9. Total = 72 ✓

Question 4: Three consecutive even numbers summing to 234

Let the three consecutive even numbers be: n, n+2, n+4

n + (n+2) + (n+4) = 234
3n + 6 = 234
3n = 228
n = 76

The numbers are: 76, 78, 80

Check: 76 + 78 + 80 = 234 ✓

Question 5: Ages of Mary, her father, and grandfather

Let Mary's age = M
Father's age = F
Grandfather's age = G

Given:
- Father is 26 years younger than grandfather: F = G - 26
- Father is 29 years older than Mary: F = M + 29
- Sum of all ages = 135: M + F + G = 135

From F = M + 29, we get M = F - 29
From F = G - 26, we get G = F + 26

Substitute into sum equation:
(F - 29) + F + (F + 26) = 135
3F - 3 = 135
3F = 138
F = 46

Therefore:
M = 46 - 29 = 17
G = 46 + 26 = 72

Check: 17 + 46 + 72 = 135 ✓
Father (46) is 26 years younger than grandfather (72) ✓
Father (46) is 29 years older than Mary (17) ✓

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Final Answer:

Question 1:
A) x = 4
B) y = -10

Question 2: The original numbers are 15 and 25

Question 3: There are 72 deer in the herd

Question 4: The three consecutive even numbers are 76, 78, and 80

Question 5:
- Mary is 17 years old
- Mary's father is 46 years old
- Mary's grandfather is 72 years old