91Ó°ÊÓ

The number of $\$0.56$stamps she bought was $10$ less than four times the number of$\$0.41$ stamps. Yumi spent$\$34.15$ in buying stamps. We have to find the number of each stamp she purchased.

Let xbe the number of $\$0.41$stamps.

Now, the number of $\$0.56$stamps was $10$less than four times the number of $\$0.41$stamps.

So, the number of $\$0.41$stamps is $4x-10.$

Thus, the table is

The total value of stamps is$34.15.

Write the equation by adding the total value of all the types of coins.

So,$0.41\left(x\right)+0.56(4x-10)=34.15.$

By proceeding with the equation we get,

$$\begin{gathered} 0.41\left(x\right)+0.56(4x-10)=34.15 \\ 0.41x+2.24x-5.6=34.15 \\ 2.65x=39.75 \\ x=15 \end{gathered}$$

Thus, the number of $\$0.41$stamps is $15$and the number of $\$0.56$stamps is$4\left(15\right)-10=50.$

To check the answer replace xby $15$into the original equation.

$$\begin{gathered} 0.41\left(15\right)+0.56(4\left(15\right)-10)=34.15 \\ 6.15+33.6-5.6=34.15 \\ 34.15=34.15 \end{gathered}$$

It is true.

The number of $\$0.41$stamps is $15$and the number of $\$0.56$stamps is$50.$