Question

The larger number is five more than the smaller number. Four more than three times the

smaller number is twice the larger number. Find both numbers.

Answer 1

6 and 11

Explanation:

x ← the smaller number

x+5 ← five more than the smaller number - the larger number

3x ← three times the smaller number

3x+4 ← four more than three times the smaller number

2(x+5) ← twice the larger number

3x + 4 = 2(x + 5)

3x + 4 = 2x + 10

-4 -4

3x = 2x + 6

-2x -2x

x = 6

x+5 = 6 + 5 = 11

Check: 3•6 + 4 = 22; 22:2 = 11

Answer 2

Larger number = 11

Smaller number = 6

Explanation:

Let the larger number = x

Let the smaller number = y

x - y = 5

3y + 4 = 2x Subtract 2x

-2x + 3y + 4 = 0

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Multiply the first equation by 2. Write the second equation underneath

2x - 2y = 10

-2x + 3y + 4 = 0

add

y + 4 = 10

Subtract from both sides

y = 10 - 4

y = 6

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x - y = 5

x - 6 = 5 Add 6 to both sides

x = 5 + 6

x = 11