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During her shift at the museum ticket booth, Leah sold 115 tickets for a total of $1,163. Adult tickets cost $12 and student tickets cost $5. How many adult tickets and how many student tickets did Leah sell?
84 adult tickets, 31 student tickets
A whale-watching ship had 40 paying passengers on board. The total collected from tickets was $1,196. Full-fare passengers paid $32 each and reduced-fare passengers paid $26 each. How many full-fare passengers and how many reduced-fare passengers were on the ship?
26 full-fare, 14 reduced fare
Now, we’ll do one where we fill in the table all at once.
Monica paid $8.36 for stamps. The number of 41-cent stamps was four more than twice the number of two-cent stamps. How many 41-cent stamps and how many two-cent stamps did Monica buy?
The types of stamps are 41-cent stamps and two-cent stamps. Their names also give the value!
“The number of 41-cent stamps was four more than twice the number of two-cent stamps.”
Eric paid $13.36 for stamps. The number of 41-cent stamps was eight more than twice the number of two-cent stamps. How many 41-cent stamps and how many two-cent stamps did Eric buy?
32 at $0.41, 12 at $0.02
Kailee paid $12.66 for stamps. The number of 41-cent stamps was four less than three times the number of 20-cent stamps. How many 41-cent stamps and how many 20-cent stamps did Kailee buy?
26 at $0.41, 10 at $0.20
Now we’ll solve some more general applications of the mixture model. Grocers and bartenders use the mixture model to set a fair price for a product made from mixing two or more ingredients. Financial planners use the mixture model when they invest money in a variety of accounts and want to find the overall interest rate. Landscape designers use the mixture model when they have an assortment of plants and a fixed budget, and event coordinators do the same when choosing appetizers and entrees for a banquet.
Our first mixture word problem will be making trail mix from raisins and nuts.
Henning is mixing raisins and nuts to make 10 pounds of trail mix. Raisins cost $2 a pound and nuts cost $6 a pound. If Henning wants his cost for the trail mix to be $5.20 a pound, how many pounds of raisins and how many pounds of nuts should he use?
As before, we fill in a chart to organize our information.
The 10 pounds of trail mix will come from mixing raisins and nuts.
We enter the price per pound for each item.
We multiply the number times the value to get the total value.
Notice that the last line in the table gives the information for the total amount of the mixture.
We know the value of the raisins plus the value of the nuts will be the value of the trail mix.
| Write the equation from the total values. |
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| Solve the equation. |
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| Find the number of pounds of nuts. |
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| 8 pounds of nuts | |
| Check.
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| Henning mixed two pounds of raisins with eight pounds of nuts. |
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