Mrs. Boyer’s 7th Grade Weblog

Problem #1:
Julie is creating a scale model of her bedroom to help her decide how to rearrange her furniture.  Her actual bedroom is 12 feet by 15 feet.  She has a shoebox that is 4 inches wide that she can cut to be the correct length.  She plans to use the following proportion to help her figure out how long to make the shoebox:

Feet        12     =      15
Inches     4               x

Then Julie uses cross multiplication to find the equation 12x = 60.  She solves it by dividing both sides by 12 which produces x = 5.  She should cut the shoebox to be 5 inches long.

Problem #2:
Mrs. Boyer has to drive to Lancaster to visit her grandmother.  She has a map with scale 1 cm: 10 miles.  She measures that it is approximately 10 centimeters from Lewisburg to Lancaster.  She uses the following proportion to help her figure out how far it is:

Centimeters    1    =    10
Miles              10          x

Then she cross-multiplies to get the equation x = 100 which tells her that it is 100 miles to Lancaster.  Then she knows that her car gets 23 miles per gallon, and gas is currently $3.35 per gallon.  She wants to estimate how much it will cost her to drive to Lancaster, so she uses the following proportion:

Miles        23    =    100
Gallons     1              x

She cross-multiplies to get the equation 23x=100.  She divides both sides by 23 to find that she will use about 4.3 gallons of gasoline.  Then she uses the following proportion:

Dollars        3.35    =    x
Gallons         1            4.3

She cross-multiplies to get x=14.405, so she knows it will cost about $14.41 to buy gas for her trip to Lancaster.