How to Solve Mixture Word Problems

Many mixture word problems involve combining two or more items and then determining either the percentage or the price of the resulting mixture. To solve mixture word problems, you need to find some sort of relationship about the mixture and then put this information into an equation.

Instructions

1. Create a 20 pound mixture of strawberry gumdrops and pineapple jellybeans where the gumdrops sell at $0.95 per pound and the jellybeans sell at $1.20 per pound. Calculate the pounds of each candy you should use in the mix if you want to sell this mix at $1.10 per pound.

2. Let X represent the amount of gumdrops in pounds. Since gumdrops sell for $0.95 per pound, then you find the total cost in dollars by multiplying X pounds and $0.95/pound i.e. (0.95/pound) x(X pounds.) Let 0.95 X equal A.

3. Represent the amount of jellybeans in pounds as (20-X) because we know the total mix is 20 pounds. Similarly as in Step 2, the total cost in dollars for the jellybeans is (1.20) x (20-X) and designate this as B.

4. Find the total cost of the mixture by multiplying 20 pounds by $1.10/pound or (20) x (1.10) = $22.00 and let this be C.

5. Use the information from Step 2, Step 3 and Step 4 and solve the equation A+B=C or [0 .95X + 1.20(20-X)] = 22.00.

6. Simplify the equation in Step 5 by first using the distributive property and then adding like terms to get -0.25 X +24.00 = 22.00. Subtract 24.00 from both sides of the equation and you get that -0.25X = -2.00. Now divide both sides by -0.25 to solve for X and find that X=8.

7. See that in Step 2 the X=8 represents the amount of gumdrops in pounds needed for this mix and then substituting into the equation (20-X) in step 3 you get that 20-8 = 12 which is the amount of jellybeans in pounds needed for the mixture. By finding these two values, you have solved this mixture word problem.