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put this solution on YOUR website!The sum of two numbers is 29. If the smaller is doubled and the larger is increased by 7, the resulting numbers will be equal. Find both numbers.
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Let x = smaller number
and y = larger number
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Since we have two unknowns, we need two equations:
From:"The sum of two numbers is 29" we get equation 1:
x + y = 29
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From:"If the smaller is doubled and the larger is increased by 7, the resulting numbers will be equal." we get equation 2:
2x = y + 7
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Using the "substitution method", solve equation 1 for y:
x + y = 29
y = 29 - x
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Substitute the above into equation 2 and solve for x:
2x = y + 7
2x = 29 - x + 7
3x = 29 + 7
3x = 36
x = 12 (smaller number)
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To find the larger number, substitute the above into equation 1 and solve for y:
x + y = 29
12 + y = 29
y = 29 - 12
y = 17 (larger number)
