# Math Help - coins/inequality word problem

1. ## coins/inequality word problem

Bridgett has 64 coins in nickels and dimes. What is the minimum number of dimes she should have to have at least $4.55? Set up the inequality and solve. Thanks 2. Hello, eunabug! Bridgett has 64 coins in nickels and dimes. What is the minimum number of dimes she should have to have at least$4.55?
Set up the inequality and solve.

Let: . $\begin{bmatrix}n &=& \text{number of nickels} \\ d &=& \text{number of dimes}\end{bmatrix}$

Then: . $n + d \:=\:64 \quad\Rightarrow\quad n \:=\:64-d$ .[1]

The value of the coins is: . $5n + 10d$ cents
. . which is to be at least 455 cents.

We have: . $5n + 10d \:\ge \:455$ .[2]

Substitute [1] into [2]: . $5(64-d) + 10d \:\ge \:455$

. . $320 - 5d + 10d \:\ge \:455 \quad\Rightarrow\quad 5d \:\ge\:135 \quad\Rightarrow\quad d \:\ge\:27$

Therefore, Bridgett should have at least 27 dimes.