Mixture & Money Problems Algebra Honors John has $1.70, all in dimes and nickels. He has a total of...
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Transcript of Mixture & Money Problems Algebra Honors John has $1.70, all in dimes and nickels. He has a total of...
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 = 1.70BACK
7.105.10.
22
nd
nd
170510 100 ndM-10
2201010 - nd
505 n10n12d
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 = 196BACK
A + C = 50
5A + 3C = 196-3A – 3C = -150
-3
2A = 46
A = 23
23 + C = 50
C = 27
5(23) + 3(27) = 196
115 + 81 = 196
23 Adults and27 Children
Check
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
.20x + .50y = .30(12).30(12)= 3.6
BACK
x + y = 12
.20x + .50y = 3.62x + 5y = 36
10
-2x – 2y = -24
3y = 12
x + (4) = 12
x = 8
.2(8) + .5(4) = 3.6
1.6 + 2 = 3.6
8 gallons of 20%4 gallons of 50%
Check
-2
y = 4
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 Total
Colum
Flavor
Mix
Let’s fill in the chart with what we know.
5 4.50
x 3.00
4.00
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 Totals
Colum
Flavor
Mix
5 4.50
x 3.00
4.00x + 5
22.5
3x
Equation
The equation comes from the vertical and horizontal totals.BACK
He will need 2.5 lbs of the flavored coffee.
5435.22 xx
20435.22 xx
205.22 x
x5.2
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 Amount
% Acid Amnt of Acid
Original Solution
Water
New Solution
300 60%
x 0%
45%300 + x
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)
BACK
rRaisinsnNuts
20 nr
8075.45.3 nr
Mixture & Money Problems
Algebra Honors