Page 159 - Math Course 2 (Book 2)

Understanding Weighted Averages

Original Write and solve an equation using the information
8.75 + 0.5w = 1.00(5 + w)
equation in the table.
Distributive
8.75 + 0.5w = 5.0 + 1w Amount of amount of amount of
Property antifreeze in antifreeze in antifreeze in
Subtract 35% solution plus 100% solution equals 50% solution.
8.75 + 0.5w – 0.5w = 5.0 + 1w – 0.5w 0.5w from 0.35(2) + 1.0(g) = 0.50(2 + g)
side
Original
8.75 = 5.0 + 0.5w Simplify. 0.35(2) + 1.0(g) = 0.50(2 + g)
equation
Subtract 5.0 Distributive
8.75 – 5.0 = 5.0 + 0.5w – 5.0 from each 0.70 + 1g = 1 + 0.50g Property
side
Subtract
3.75 = 0.5w Simplify. 0.70 + 1g – 0.50g = 1 + 0.50g – 0.50g 0.50g from
side

3.75 = 0.5w Divide each 0.70 + 0.50g = 1 Simplify.
0.5 0.5 side by 0.5.
Subtract 0.70
7.5 = w Simplify. 0.70 + 0.50g – 0.70 = 1 – 0.70 from each
side.

Jeri should buy 7.5 pounds of 0.50g = 0.30 Divide each
cheaper cat food to be mixed 0.50 0.50 side by 0.50
Answer with the 5 pounds of gourmet cat
food to equal out to $1.00 per g = 0.60 Simplify.
pound of cat food

Darryl should add 0.60 gallons
Answer of 100% antifreeze to produce a
Percents
50% solution.
Examples

Your Turn!
AUTO MAINTENANCE
A car’s radiator should contain a solution of 50% Prices
antifreeze. Darryl has 2 gallons of a 35% anti-
freeze. How many gallons of 100% antifreeze Cheryl bought 3 ounces of glass beads that cost
should Darryl add to his solution to produce a $1.79 an ounce. The seed beads cost $0.99 an
solution of 50% antifreeze? ounce. How many ounces of seed beads can she
buy if she only wants the beads to be $1.29 an
Let g = the number of gallons of 100% antifreeze ounce for her craft project?
to be added. Make a table.
A. 3.1 ounces
Amount of Amount of B. 5 ounces
solution(gal.) Antifreeze C. 4.6 ounces
D. 2 ounces
35% Solution 2 0.35(2)
Answer
100% Solution g 1.0(g)

50% Solution 2 + g 0.50(2 + g)

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