Chapter 6, Problem 2MPS

To determine

Solve the problem if it has a solution.

Answer to Problem 2MPS

No solution.

Explanation of Solution

Given:

C has 20 coins worth $3.15.If the coins are dimes and quarters only , find the number of each type of coin.

Calculation:

1 dime =10 cents

1 quarter = 25 cents

Let the number of dimes = x

Let the number of quarters = y

Since C has 20 coins in total , so , x + y = 20

And in total , they sum up to $3.15 = 315 cents

  $\begin{array}{l}10x+25y=315\\ \Rightarrow 10(25-y)+25y=\mathrm{315......}[x=25-y]\\ \Rightarrow 250-10y+25y=315\\ \Rightarrow 15y=315-\mathrm{250................}[\text{subtract 250 from each side]}\\ \Rightarrow 15y=115\\ \Rightarrow y=\frac{115}{15}\mathrm{............................}[\text{divide each side by 15]}\\ \Rightarrow y=\frac{23}{3}\end{array}$

Since the number of coins should be whole number , but here it is not.

Hence the problem has no solution.