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