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Example 2
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L
A n auto mechanic has 300 m L of battery acid solution that is 60% acid. He
must add water to this solution to dilute it so thai it is only 459c acid. How
much water should he add?
Soiution
Step 1 The problem asks for the number of milliliters of water to be added.
Step 2 Let .1 = the number of milliliters of water to be added.
1
Total amount x % acid = Amount of acid
Original solution
Water
New solution
300
bO^k
X
0%
300 f
'
0
0,45(300 + X)
45%
X
0.60(3(X)l
Step 3 Original amount of acid + added acid = new amount of acid
0.45i-^("M) * X)
0
0.60(300)
601300)
18,000
4500
100
Step 4
= 43(300 + x)
= 13.500 + 45.V
= 45x
= X
Siep 5 The check is left to you.
.-. 100 m L of water should be added
Answer
Examples 1 and 2 are really very much alike. You can see this in the
charts and in Step 3 of each .solution. In fact, mixture problems arc similar to
investment problems, coin problems, and certain distance problems.
Oral Exercises
Read each problem and complete the chart. Use the chart to give an
equation to solve the problem. Do not solve.
L
The owner of the Fancy Food Shoppe wants to mix cashews selling at
.S8 00/kg and pecans selling at S7.00/kg. How many kilograms of each
kind of nut should be mixed to get 8 kg worth $7.25 kg?
Number of kg x Price per kg = Total cost
Cashews
322
Pecans
^. 00
Mixture
1. j t g
Chapter 7
ex
3Ea
2. A chemist has 40 m L of a solution thai is 5 0 ^ acid. How much water
should he add to make a solution thai is 10% acid?
:
Original solution
4t> i
X
Water added
New solution
so
e
\'0
; 0
3. I f 80*} m L (>f a juice drink is IS";;- grape juice, how much grape juice
should be added to make a drink that is 20'* grape juice?
Total amount x
=
\^
( vo
Original drink
Juice added
% juice
X
Amount of juice
iCOK
\
New drink
4. A chemist mixes 12 L of a solution that is 45'??^ acid with 8 L of a solution
that is 70% acid. What is the percent of acid of the mixture?
Total amount <•
1st Solution
2nd Solution
Mixture
% acid
=
Amount of acid
l-x
65%
^0
5. A grocer mixes 5 lb of egg noodles costing 80e,'lb with 2 lb of spinach
noodles costing S l . 5 0 . i h . What will the cost per pound of the mixture be?
Number of lb x
Cost per lb
=
Total cost
Egg noodles
/ AD
Spinach noodles
Mixture
W ., J
.r
ft. Susan drove lor 2 li at 85 Km'h and then for 3 h more at 95 knVh. What
was her average speed for the entire trip?
Rate
X
Time
=
Distance
1st part of trip
2nd part of trip
Entire trip
X
1
323
7. Sam invested S2000 at 5 i % amiual interest and $3000 at 8 i % annual interest. What percent interest is he earning on his total investment?
Amoimt invested x Rate = Interest
ooo[ ^ J ^ ) i-3oeo{f'^)'
Investment A
.0
3VOO
Investment B
Total Investments
5' voo
X
8. Gina has a pile of 50 dimes and nickels worth $'1.30 How many coin*; of
each type does she have?
Number of coins x Value per coin = Total value
fO
Dimes
Nickels
50
^6
^ -4)
Collection
Problems
A
1-8. Solve the problems in Oral Exercises 1-8.
Solve.
9. How many liters of water must be added to 50 L of a 30% acid solution in
order to produce a 20% acid solution?
10. How many milliliters of water must be added lu 60 m L of a 15% iodine
solution in order to dilute it to a 10% iodine solution?
11. A spice mi.Kture is 2 5 % thyme. How many grams of thyme must be added
to 12 g of the mixture to increase the thyme content to 40%?
12. A grocer mixes two kinds of nuts. One kind costs S5.00/kg and the other
S5.80'kg. How many kilograms of each type are needed to make 40 kg of
a blend woith S.-^-SO/kg?
13. Joanne makes a mixture of dried fruits by mixing dried apples costing
$6.00/kg with dried apricots costing $8.00/kg. How many kilograms of
each are needed to make 20 kg of a mixture worth S7.20/kg?
/5
14. A farm stand owner mixes apple juice and cranberry juice. How mirch
should he charge i f he mixes 8 L of apple juice selling for 45(i'L with 10 L
of cranberry juice selling for $l.08,'L?
15. I f you drive for 2 h at 80 knv'h, how fast must you drive during the ne.xt
hour in order to have an average speed of 75 km/h?
324
Chapter 7
din^,
16. I f Sylvia works overtime, she is paid l i times as much per hour as usual.
After working her usual 40 h last week, she worked an additional 4 h overtime I f .she made $552 last week, find her usual hourly wage.
B
17. A chemist wishes to mix some pure acid with .some water to produce 16 L
of a solution that is 30% acid. How much pure acid and how much water
should be mixed?
18. How many liters of water must be evaporated from 10 L of a 40% salt solution to produce a 50% solution?
19. How many liters of water must be evap<irated from 20 L of a 30% salt solution to produce a 50% solution?
20. A wholesaler has 100 kg of mixed nuts that sell for H.W/kg. In order to
make the price more attractive, she plans to mix in some cheaper nuts
worth .$3.20/kg. I f thejvliolesaler wants to sell the mixture for $3.40/kg,
how many kilograms of the cheaper nuts should be used?
21. A securities broker advised'a client to invest a total of $21,000 in bonds
paying 12% interest and in certificates of deposit paying 5 i % interest. The
annual income from these irivestuienis was "S2250. Find out how much was
invested at each rate.
22. A collection of 50 coins is worth S5.20. There are 12 more nickels than
dimes, and the rest of the coins are quarters. How many coins of each type
are in the collection?
23. (a) I f you bike for 2 h at 30 km/h and for 2 h ;« 20 km;'h. what is your
average speed for the whole trip? (b) If you bike for 60 km at 30 k m h and
rentm at 20 km/h, what is your average speed for the whole trip?
C
^
24. The ratio of nickels to dimes to quarters is 3 : 8 : 1 . I f all the coins were
dimes, the amount of money would be the same. Show that there are infinitely many solutions to this problem.
25. A grocer wants to make a mixture of three dried fruits. He decides that the
ratio of pounds of banana chips to apricots to dates should be 3 : 1 1 , B a nana chips cost $1.17/lb, apricots cost $3.00;Ib. and dates cost $2.30/lb.
What is the cost per pound of the mixture?
Mixed Review Exercises
Evaluate.
1. 9% of 60 -f 0.4% of 230
2. What percent of 45 is 18?
3. What percent of 160 is 12?
4. 16 is \2\%
of what number?
Evaluate if a = 2. ft = 3. x = 5. and y = 4.
5.
-51 +
V
6.
1 -2b
i +b
7. | ( 9 . t
+
v)
8,
.n-^
9. 2a + 5b
10. {x - b)-
325
Mi- ^
2x r
02^J525^^-^^^
Mood
^
as" i
(2^
10
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