### math_powerpoint - AQUINAS

```Mixture Problems
What is a mixture problem?
• Word problems where items or quantities of
different values are mixed together
Mixture Problems + Real Life
• After learning quite a bit of information about
mixture problems, I’ve found that they can be
most useful to business owners who are trying
to figure out what they need to use to make a
certain profit
• Mixture problems can also be used for all
kinds of science problems, chemistry in
particular
Problem #1
• Mr. Wilson wrote down his daily black cow
root beer float sales for the last week. He had
sold 414 floats at \$2.15 each. The ingredients
for the floats cost \$1.08 per float. How much
profit did he make last week?
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414*2.15 = 890.1
414*1.08 = 447.12
890.1 – 447.12 = 442.98
Mr. Wilson’s total profit was \$442.98
Problem #2
• 9 lbs of mixed nuts containing 55% peanuts was
mixed with 6 lbs of another kind of mixed nuts that
contains 40% peanuts. What percent of the new
mixture is peanuts?
• .55*9 + .40*6=15x
• 4.95 + 2.4 = 15x
• 7.35 = 15x
• X = 7.35/15
• X = .49 or 49% of the new mix is peanuts
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.55*9 + .40*6=15x
4.95 + 2.4 = 15x
7.35 = 15x
X = 7.35/15
X = .49 or 49% of the new mix is peanuts
Problem #3
• Brand X sells 21 oz. bags of mixed nuts that
contain 29% peanuts. To make their
product they combine Brand A mixed nuts
which contain 35% peanuts and Brand B
mixed nuts which contain 25% peanuts.
How much of each do they need to use?
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Let a = ounces of brand A nuts used
Let b = ounces of brand B nuts used
.35a +.25b/21 = .29
.35a + .25b = .29 * 21
(1) .35a + .25b = 6.09
(2) A + B = 21
#3 continued
• Now we multiply both sides of (2) by .25 and
then we subtract (2) from (1)
• 21*.25 = 5.25
• (1) .35a + .25b = 6.09
• (2) .25a + .25b = 5.25
• 6.09 – 5.25 = .84 = .1a
• A = 8.4
#3 continued
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A + B = 21
8.4 + B = 21
21 – 8.4 = 12.6
B = 12.6
8.4 + 12.6 = 21
```