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
Hello, eunabug!
Bridgett has 64 coins in nickels and dimes.
What is the minimum number of dimes she should have to have at least $4.55?
Set up the inequality and solve.
Let: .$\displaystyle \begin{bmatrix}n &=& \text{number of nickels} \\ d &=& \text{number of dimes}\end{bmatrix}$
Then: .$\displaystyle n + d \:=\:64 \quad\Rightarrow\quad n \:=\:64-d$ .[1]
The value of the coins is: .$\displaystyle 5n + 10d$ cents
. . which is to be at least 455 cents.
We have: .$\displaystyle 5n + 10d \:\ge \:455$ .[2]
Substitute [1] into [2]: .$\displaystyle 5(64-d) + 10d \:\ge \:455 $
. . $\displaystyle 320 - 5d + 10d \:\ge \:455 \quad\Rightarrow\quad 5d \:\ge\:135 \quad\Rightarrow\quad d \:\ge\:27$
Therefore, Bridgett should have at least 27 dimes.