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put this solution on YOUR website!The sum of two integers is thirty. Eight times the smaller integer is six more than five times the larger integer. Find the integers.
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Assign variables to things you don't know.
Let x = larger integer
and y = smaller integer
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Since we have two unknowns, we'll need to find two equations.
From: "The sum of two integers is thirty." we get equation 1:
x+y = 30
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From: "Eight times the smaller integer is six more than five times the larger integer." we equation 2:
8y = 5x+6
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To solve, let's solve equation 1 for 'x':
x+y = 30
x = 30-y
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Substitute the above into equation 2 and solve for y:
8y = 5x+6
8y = 5(30-y)+6
8y = 150-5y+6
13y = 150+6
13y = 156
y = 156/13
y = 12 (value of smaller integer)
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Substitute the above into equation 1 and solve for x:
x+y = 30
x+12 = 30
x = 30-12
x = 18 (value of larger integer)
