Transcript Mixture Problems - Sylmar High School

Mixture & Money Problems
Algebra Honors
John has $1.70, all in dimes and
nickels. He has a total of 22 coins.
How many of each kind does he have?
Let d = number of dimes
Let n = number of nickels
Counting equation
d + n = 22
Value equation
.10d + .05n = 1.70
BACK
d  n  22
.10d  .05n  1.7
-10
M100 10d  5n  170
- 10 d  10 n  220
 5n  50
n  10
d  12
Tickets to a movie cost $5.00 for adults and $3.00
for children. If tickets were bought for 50 people for
a total of $196 how many adult tickets were sold and
how many children tickets were sold?
Let A = the number of Adult tickets
sold.
Let C = the number of children tickets
sold.
Counting Equation
A + C = 50
Value Equation
5A + 3C = 196
BACK
-3
A + C = 50
5A + 3C = 196
-3A – 3C = -150
2A = 46
23 + C = 50
C = 27
23 Adults and
27 Children
A = 23
Check
5(23) + 3(27) = 196
115 + 81 = 196
How much 20% alcohol solution and 50%
alcohol solution must be mixed to get 12
gallons of 30% alcohol solution?
Let x = amount of 20%
Let y = amount of 50%
Counting Equation
x + y = 12
Value Equation
.30(12)= 3.6
.20x + .50y = .30(12)
BACK
-2
10
x + y = 12
.20x + .50y = 3.6
2x + 5y = 36
-2x – 2y = -24
x + (4) = 12
x=8
8 gallons of 20%
4 gallons of 50%
3y = 12
y=4
Check
.2(8) + .5(4) = 3.6
1.6 + 2 = 3.6
BACK
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 = amount 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
Total
4.00
Let’s fill in the chart with what we know.
BACK
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
Colum
5
4.50
Flavor
x
3.00
Mix
x + 5 

4.00
Totals
22.5
 3x

Equation
The equation comes from the vertical and horizontal totals.
BACK
22.5  3x  4x  5
22.5  3x  4 x  20
22.5  x  20
2 .5  x
He will need 2.5 lbs of the flavored coffee.
BACK
An auto mechanic has 300 mL of battery acid
solution that is 60% acid. He must add water to
the solution to dilute it so that it is only 45% acid.
How much water should he add?
Total
% Acid Amnt of
Amount
Acid
Original
Solution
Water
New
Solution
300
60%
x
0%
300 + x
45%
180
0
Equation
Equation: 180 = 0.45 (300 + x)
BACK
A health food store sells a mixture of raisins and
roasted nuts. Raisins sell for $3.50/kg and nuts
sell for $4.75/kg. How many kilograms of each
should be mixed to make 20 kg of this snack
worth $4.00/kg? (Write Equation Only)
Raisins  r
Nuts  n
r  n  20
3.5r  4.75n  80
BACK
Mixture & Money Problems
Algebra Honors