# Carrie has 27 coins in her purse. All the coins are 5 cent or 20 cent coins. If the total value...

Carrie has 27 coins in her purse. All the coins are 5 cent or 20 cent coins. If the total value of the coins is $3.75, how many of each type does she have? ## Word Problems: In multi-step problems, the main concern would be in keeping track of the equations that can be used in the solution. Labelling each equation properly and representing the variables in a way that makes sense in the solution would greatly help in solving the problem. ## Answer and Explanation: Let • {eq}F {/eq} represent the number of five cent coins • {eq}T {/eq} represent the number of twenty cent coins. Carrie has 27 of these coins in her purse, as an equation it would be: {eq}F + T = 27 \ \ \ \ \rm Eq. \ 1 {/eq} The total value of the coins in her purse is$3.75 and as an equation it would be:

{eq}0.05 F + 0.20 T = \\$3.75 \ \ \ \ \rm Eq. \ 2 {/eq}

Solving for {eq}F {/eq} from Eq. 1:

{eq}\begin{align} F + T &= 27 \\ F &= 27 - T \ \ \ \ \ \rm Eq. \ 3 \end{align} {/eq}

Substituting Eq. 3 in Eq. 2:

{eq}\begin{align} 0.05 F + 0.20 T &= 3.75 \\ 0.05(27 - T) + 0.20 T &= 3.75 \\ 1.35 - 0.05T + 0.20 T &= 3.75 \\ 0.15T &= 3.75 -1.35 \\ \dfrac {0.15T}{0.15} &= \dfrac{2.4}{0.15} \\ T &= 16 \end{align} {/eq}

Substituting the value of the number of 20 cent coins in Eq. 3:

{eq}F = 27 - T \\ F = 27 - 16 \\ F = 11 {/eq}

There are 11 pieces of the 5-cent coins and 16 pieces of the 20-cent coins. 