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? Let’s fill in the chart with what we know x

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 x x x 4(x + 5) The equation comes from the Total Column: 1st + 2nd = 3rd

x = 4(x + 5) x = 4x x - 3x = 4x - 3x = x = x = 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 $ in interest in the first year, how much should he place in each account?

x x Fill in the cells with what you know. Don’t click until you have Filled in the cells on paper..115x. 09(15000-x) 15,

x x.115x.09( x) The equation comes from the Interest Column: 1st + 2nd = 3 rd Work it out first, then click to check.115x +.09( x) = x x = x = x = x = = 6500 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 pounds of pecans 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% /3 hours at Job 1 and 34 2/3 hours at Job hours by the carpenter and 38 hours of work by the painter. For complete details click to next slide.

x = 6.48(x + 20) x = 6.48x = 6.48x – 5.4x – = 1.08x 32.4 = 1.08x 30 = x 50 = x pounds of pecans will need to be added to the 20 pounds of macadamia nuts to make a mix worth $ 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? lbscosttotal macd pecansx x X (x+20)

5.4x + 4.4(40 – x) + = 40(4.8) 5.4x +176 – 4.4x + = 192 x = 192 x = – x = 24 Mr. Plantar will need 16 lbs of pecans and 24 lbs of walnuts to make a mix of 40 lbs. worth $ 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? lbscosttotal Pecansx x walnuts40 - x (40-x) (40)

.08x +.11(2400 – x) = x x = x = x = - 24 x = 800, = 1600 Eddie invested $800 in the 8% account and $1600 in the 11% account. 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? PRInt 8%x.08.08x 11% x.11.11(2400-x)

Each account earned the same interest, thus.07x =.06(12500 – x).07x = x.13x = 750 x = = = 6731 Check:.07(5769) = $ (6731) = $ Why do you think there is a difference here of 3 cents? 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. PRInt 7%x.07.07x 6% x.06.06(12500-x) 12,500

7.5x – 9x = x = -23 x = 15 1/3 hours at Job 1 and 50 – 15 1/3 = 34 2/3 hours at Job 2 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? hoursrateTotal Job 1x x Job 250- x9.00 9(50 – x)

18x + 15(73 – x) = x – 15x = x = 105 x = 35 hours for the carpenter = 38 for the painter 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? hoursrateTotal Painterx15 15x Carpenter 73- x18 18(73 – x)

The last lesson for this unit is motion problems. Go to the lesson index.lesson index