More Rate Comparisons
Student Summary
Sometimes we can find and use more than one unit rate to solve a problem.
Suppose a small bag of powder detergent holds 16 ounces and is sold for $2. A large bag that holds 2 kilograms is sold for $8. Which is a better deal?
Because the bags are in different units of weight, it helps to make comparisons using the same unit. Here are two different ways:
Compare the price per kilogram:
- The large bag costs $8 for 2 kilograms, so it costs $4 per kilogram (8÷2=4).
- The small bag holds 16 ounces or 1 pound of detergent, so it costs $2 per pound. At this rate, the cost is 2⋅(2.2) or $4.40 per kilogram (since there are about 2.2 pounds in 1 kilogram).
The large bag is a better deal, because it costs less money for the same amount of detergent.
Compare the weight of detergent per dollar:
- With the small bag, we get 1 pound of detergent for $2 or 0.5 pound per dollar.
- With the large bag, we get 2 kilograms of detergent for $8 or about 4.4 pounds for $8. This means we get (4.4)÷8, or 0.55, pound per dollar.
The large bag is a better deal, because we get more detergent for the same amount of money.
Another way to solve the problem would be to compare the unit prices of each bag in dollars per ounce. Try it!
Visual / Anchor Chart
Standards
Addressing
6.RP.3
6.RP.A.3
6.RP.3.b
6.RP.A.3.b
Building Toward
6.RP.3.c
6.RP.A.3.c