coins/inequality word problem

**eunabug** · September 9th 2010, 11:47 AM

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

**Soroban** · September 9th 2010, 12:22 PM

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.

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