# Solve Application Problems

How many nickels and how many pennies does Jesse have? The number of nickels is defined in terms of the number of pennies, so start with pennies. $$\begin 7(0.01) 59(0.05) &\overset 3.02 \nonumber \ 3.02 &= 3.02\checkmark \nonumber \ \end$$ Example $$\Page Index$$ Jesse has .55 worth of quarters and nickels in his pocket.

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How many 49-cent stamps and how many 20-cent stamps did Kailee buy?

In most of our examples so far, we have been told that one quantity is four more than twice the other, or something similar.

The number of dimes times the value of each dime equals the total value of the dimes.

$\begin \textit·\textit &= \textit \nonumber\\ 23·0.10 &= 2.30 \nonumber\\ \end \nonumber$ This method leads to the following model.

How many children’s tickets and how many adult tickets did he sell?

Now we’ll solve some more general applications of the mixture model.Example $$\Page Index$$ Kailee paid .74 for stamps.The number of 49-cent stamps was four less than three times the number of 20-cent stamps.Adult tickets cost and student tickets cost .How many adult tickets and how many student tickets did Leah sell?Example $$\Page Index$$ Jesse has .02 worth of pennies and nickels in his piggy bank.The number of nickels is three more than eight times the number of pennies. Represent the number of each type of coin using variables.Using algebra to find the number of nickels and pennies in a piggy bank may seem silly.You may wonder why we just don’t open the bank and count them.How many nickels and how many quarters does Jesse have?Example $$\Page Index$$ Elane has .00 total in dimes and nickels in her coin jar.

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