1. 8.2 Problem Solving with Proportions

2. 8.2 Problem Solving with Proportions
Power Standard #4
Use the properties of similarity and the concepts of ratio
and proportion to solve problems (1.1.4)
Power Standard #12
Use the characteristics and properties of right triangles
to solve problems (1.3.1, 1.3.2)

3. Properties of Proportions
Given:
Cross Product
Property
Reciprocal
Property
May be rates as well as ratios.
Interchange Means
Property
Nameless
Property OE

4. Solving Problems involving Proportions
The ratio of pounds of potatoes to gallons of soup is 2:5. If 125 pounds of potatoes are used, how large is the batch of soup?
Verbal Model Ratio
Given Constant Ratio
Present Ratio
pounds
2 pounds
125 pounds ; =
gallons
5 gallons
312.5 gallons
x gallons

5. If the plan of a house below is drawn to a scale of 1/8 inch to 1 foot what are the dimensions of the house?
If the hallway is 3 feet wide how large should it appear on the plan? 8” 3”
actual 3’ wide

6. The ratio of Gear A to B is the same as the ratio of B to C
The ratio of Gear A to B is the same as the ratio of B to C. If Gear A has 36 teeth, Gear C has 16 teeth, how many teeth does Gear B have C B A
Note: B is said to be the geometric mean of A and B

8. In the previous slide if each window is 6’ tall what is the approximate height of the building’s wall?
Verbal Model Ratio
Given Constant Ratio
Present Ratio ; =
blocks
5 blocks
20 blocks
structure height
6 feet
x feet
24 feet
382/1 – 29, skip 24

9. Given the proportion f:r = w:b,
2/21 OE
The ratio of cement to lime to gravel in a cubic yard of concrete 5:1:32. If a batch of concrete contains 200 pounds of cement, what is the weight of the gravel?
Given the proportion f:r = w:b,
a) Write this proportion using fractions
b) Re write the proportion using the cross product property
c) Re write the proportion using the reciprocal property
d) Re write the proportion using the means interchange property
Properties