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

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) (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"
=
:
"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:
=
Cross multiply
y + 35 = 6y
35 = 6y - y
35 = 5y
y =
y = 7 is the smaller number
:
Check: larger number would be 7 + 35 = 42, we can see that:
=
;
:
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:
=
and
L * W = 216
L =
:
Substitute (216/W) for L in the ratio equation
=
Cross multiply
3W = 2*
3W =
Multiply both sides by W, get rid of the denominator and you have:
3W^2 = 432
:
W^2 =
W^2 = 144
W = , find the square root of both sides
W = 12 cm is the width
:
Check solution
L = 216/12 = 18 cm
:
= confirms our solution
:
:
Did this make sense to you? Any questions?
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