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put this solution on YOUR website!1. The ratio of two numbers in 6:1.If their difference is 35, what is the smaller number?
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Let x= a number; y = smaller number
Write an equation for each statement
"The ratio of two numbers in 6:1"
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"If their difference is 35,"
x - y = 35
x = y + 35
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what is the smaller number?
Substitute (y+35) for x in the ratio equation:
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Cross multiply
y + 35 = 6y
35 = 6y - y
35 = 5y
y =
y = 7 is the smaller number
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Check: larger number would be 7 + 35 = 42, we can see that:
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2. The ratio of the width to the length of a rectangle is 2:3. If the area of the rectangle is 216 sq. cm. , what is its width?
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Write an equation for each statement:
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and
L * W = 216
L =
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Substitute (216/W) for L in the ratio equation
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Cross multiply
3W = 2*
3W =
Multiply both sides by W, get rid of the denominator and you have:
3W^2 = 432
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W^2 =
W^2 = 144
W =
, find the square root of both sides
W = 12 cm is the width
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Check solution
L = 216/12 = 18 cm
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confirms our solution
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