SOLUTION: 1. The ratio of two numbers in 6:1.If their difference is 35, what is the smaller number? 2. The ratio of the width to the length of a rectangle is 2:3. If the area of the rectang

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Question 149008: 1. The ratio of two numbers in 6:1.If their difference is 35, what is the smaller number?
2. The ratio of the width to the length of a rectangle is 2:3. If the area of the rectanglle is 216 sq. cm. , what is its width?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can 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?
:
Let x= a number; y = smaller number
Write an equation for each statement
"The ratio of two numbers in 6:1"
x%2Fy=6%2F1
:
"If their difference is 35,"
x - y = 35
x = y + 35
:
what is the smaller number?
Substitute (y+35) for x in the ratio equation:
%28%28y%2B35%29%29%2Fy = 6%2F1
Cross multiply
y + 35 = 6y
35 = 6y - y
35 = 5y
y = 35%2F5
y = 7 is the smaller number
:
Check: larger number would be 7 + 35 = 42, we can see that:
42%2F7 = 6%2F1
;
:
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?
:
Write an equation for each statement:
W%2FL = 2%2F3
and
L * W = 216
L = 216%2FW
:
Substitute (216/W) for L in the ratio equation
W%2F%28%28216%2FW%29%29 = 2%2F3
Cross multiply
3W = 2*216%2FW
3W = 432%2FW
Multiply both sides by W, get rid of the denominator and you have:
3W^2 = 432
:
W^2 = 432%2F3
W^2 = 144
W = sqrt%28144%29, find the square root of both sides
W = 12 cm is the width
:
Check solution
L = 216/12 = 18 cm
:
12%2F18 = 2%2F3 confirms our solution
:
:
Did this make sense to you? Any questions?