Transcript No Slide Title

Mixture Problems
by
Dr. Julia Arnold
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.
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?
Amt
Cost
Colum
5
4.50
Flavor
x
3.00
Mix
4.00
Let’s fill in the chart with what we know.
Total
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
Amt
Cost
Total
Colum
5
4.50
22.5
Flavor
x
3.00
3x
Mix
x+5
4.00
4(x + 5)
The equation comes from the Total Column: 1st + 2nd = 3rd
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.
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?
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?
Principal Rate
First
Acct.
Second
Acct.
Total
x
15000 - x
15,000
Interest
.115
.115x
.09
.09(15000-x)
1562.50
Fill in the cells with what you know. Don’t click until you have
Filled in the cells on paper.
The equation comes from the Interest Column: 1st + 2nd = 3rd
.115x + .09(15000 - x) = 1562.50
Work it out first,
then click to check
.115x + 1350 - .09x = 1562.50
.025x +1350 = 1562.50
.025x = 212.50
x = 8500
15000- 8500 = 6500
Principal Rate
First
x
Acct.
Second
15000 - x
Acct.
Total
.115
.09
Interest
.115x
.09(15000 - x)
1562.50
Ron invested $8500 in the 11.5% acct. and $6500 in the 9%
acct.
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?
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?
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.
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?
macd
pecans
lbs
20
x
cost
8.10
5.40
total
X + 20
6.48
6.48(x+20)
162
5.4x
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
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?
Pecans
walnuts
lbs
x
40 - x
cost
5.40
4.40
total
40
4.80
4.8(40)
5.4x
4.4(40-x)
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.
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?
8%
11%
P
R
x
.08
2400 - x .11
Int
2400
240
.08x
.11(2400-x)
.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.
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.
7%
6%
P
R
x
.07
12500- x .06
Int
.07x
.06(12500-x)
12,500
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?
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?
Job 1
Job 2
hours
x
50- x
50
rate
7.50
9.00
Total
7.5x
9(50 – x)
427
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
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?
hours
Painter x
Carpenter 73- x
73
18x + 15(73 – x) = 1200
18x + 1095 – 15x = 1200
3x = 105
x = 35 hours for the carpenter
73- 35 = 38 for the painter
rate
15
18
Total
15x
18(73 – x)
1200
The last lesson for this unit is motion problems.
Go to the lesson index.