Mixture Problems

1
Mixture Problems by Dr. Julia Arnold
2
A typical mixture problem reads like this Joe
would like to mix 5 lbs of columbian coffee
costing 4.50 per pound with enough flavored
coffee costing 3.00 per pound to make a mix
worth 4.00 per pound. How many pounds of the
flavored coffee should he take?
Let x amt of flavored coffee in pounds
Mixture problems can be more easily solved by
using a grid.
3
Joe would like to mix 5 lbs of columbian coffee
costing 4.50 per pound with enough flavored
coffee costing 3.00 per pound to make a mix
worth 4.00 per pound. How many pounds of the
flavored coffee should he take?
5
4.50
3.00
x
4.00
Lets fill in the chart with what we know.
4
Now we fill in the remaining cells. Since we are
mixing the two types of coffee the mix Amt will
be x 5. For total multiply amt times cost and
place in total column
5
4.50
22.5
3.00
3x
x
4(x 5)
4.00
x 5
The equation comes from the Total Column 1st
2nd 3rd
5
The equation comes from the Total Column 1st
2nd 3rd
22.5 3x 4(x 5) 22.5 3x 4x 20 22.5
3x - 3x 4x - 3x 20 22.5 x 20 22.5 - 20
x 20 - 20 2.5 x
He will need 2.5 lbs of the flavored coffee.

6
Investment type problems are a type of mixture
problem. In this type of problem we are mixing
money into different accounts. For example...
Ron Brown has 15,000 to invest. He plans to
diversify his money by investing it in two
different accounts. One account gives 11.5
interest and the other 9 interest. If he wants
to make 1562.50 in interest in the first year,
how much should he place in each account?
7
Ron Brown has 15,000 to invest. He plans to
diversify his money by investing it in two
different accounts. One account gives 11.5
interest and the other 9 interest. If he wants
to make 1562.50 in interest in the first year,
how much should he place in each account?
.115
.115x
x
.09
.09(15000-x)
15000 - x
15,000
1562.50
Fill in the cells with what you know. Dont
click until you have Filled in the cells on paper.
8
The equation comes from the Interest Column 1st
2nd 3rd
Work it
out first,

then click to check
.115x .09(15000 - x) 1562.50 .115x 1350 -
.09x 1562.50 .025x 1350 1562.50 .025x
212.50 x 8500 15000- 8500 6500
x
.115
.115x
.09
15000 - x
.09(15000 - x)
1562.50
Ron invested 8500 in the 11.5 acct. and 6500
in the 9 acct.
9
Mixture Problems Work them out on paper then
check. 1. Mr. Planter wants to mix 20 lb of
macadamia nuts that cost 8.10 per pound with
pecans that cost 5.40 per pound. How many pounds
of pecans should he use if the mixture is to cost
6.48 per pound?   2. Mr. Planter also wants a
40 lb mixture of pecans and walnuts that will
sell for 4.80 per pound. If the pecans cost
5.40 per pound and the walnuts cost 4.40 per
pound, how many of each should he use?   3.
Eddie invested 2400 in two simple interest
accounts. The annual rate in one account is 8
and the annual rate in the other is 11. How much
did he invest in each account if the annual
interest totaled 240?  
10
4. Fred and Irma invested 12,500 in two simple
interest accounts. One account earns annual
simple interest of 7 while the other earns 6.
How much was invested at each rate if each
account earned the same interest? Round your
answer to the nearest dollar.   5. Bubba has two
part time jobs. One pays 7.50 per hour and the
other pays 9.00 per hour. Last week he earned
427 while working 50 hours. How many hours did
he work at each job?   6. Kim had to pay 1200
in labor for some repairs to the house. The
carpenter charged 18 an hour and the painter
charged 15 per hour. If she paid for 73 hours of
work, how much work was done by each?    
11
Mixture Solutions 1. 30 pounds of pecans 2. 16
pounds of pecans and 24 pounds of walnuts 3.
800 invested at 8. and 1600 invested at 11.
4. 5769 is invested at 7 and 6731 invested
at 6. 5. 15/3 hours at Job 1 and 34 2/3 hours
at Job 2 6. 35 hours by the carpenter and 38
hours of work by the painter.  
For complete details click to next slide.
12
1. Mr. Planter wants to mix 20 lb of
macadamia nuts that cost 8.10 per pound with
pecans that cost 5.40 per pound. How many pounds
of pecans should he use if the mixture is to cost
6.48 per pound?
 162 5.4x 6.48(x 20) 162 5.4x 6.48x
129.6 162 6.48x 5.4x 129.6 162 129.6
1.08x 32.4 1.08x 30 x 50 x 20 30 pounds
of pecans will need to be added to the 20 pounds
of macadamia nuts to make a mix worth 6.48
13
   2.   Mr. Planter also wants a 40 lb mixture
of pecans and walnuts that will sell for 4.80
per pound. If the pecans cost 5.40 per pound and
the walnuts cost 4.40 per pound, how many of
each should he use?
5.4x  4.4(40 x) 40(4.8) 5.4x 176 4.4x
192 x 176 192 x 16 40 x 24 Mr.
Plantar will need 16 lbs of pecans and 24 lbs of
walnuts to make a mix of 40 lbs. worth 4.80.
14
   3.   Eddie invested 2400 in two simple
interest accounts. The annual rate in one account
is 8 and the annual rate in the other is 11.
How much did he invest in each account if the
annual interest totaled 240?
.08x .11(2400 x) 240 .08x 264 - .11x
240 -.03x 264 240 -.03x - 24 x 800,
2400-800 1600 Eddie invested 800 in the 8
account and 1600 in the 11 account.
15
   4.   Fred and Irma invested 12,500 in two
simple interest accounts. One account earns
annual simple interest of 7 while the other
earns 6. How much was invested at each rate if
each account earned the same interest? Round your
answer to the nearest dollar.
Each account earned the same interest, thus .07x
.06(12500 x) .07x 750 -.06x .13x 750 x
5769.23 5769 12500-5769 6731 Check .07(5769)
403.83 .06(6731) 403.86 Why
do you think there is a difference here of 3
cents?
16
   5.   Bubba has two part time jobs. One pays
7.50 per hour and the other pays 9.00 per hour.
Last week he earned 427 while working 50 hours.
How many hours did he work at each job?
7.5x 450 9x 427 -1.5x -23 x 15 1/3
hours at Job 1 and 50 15 1/3 34 2/3 hours at
Job 2
17
 6. Kim had to pay 1200 in labor for some
repairs to the house. The carpenter charged 18
an hour and the painter charged 15 per hour. If
she paid for 73 hours of work, how much work was
done by each?
18x 15(73 x) 1200 18x 1095 15x
1200 3x 105 x 35 hours for the carpenter 73-
35 38 for the painter      
18
The last lesson for this unit is motion
problems. Go to the lesson index.