Question

You have quarters and dimes that total $2.80. your friends says its possible that the number of quarters is 8 more than the number of dimes. is he correct? explain

Answer 1

$\text{Let the number of dimes be x, then as per the friend the number of }\\ \text{quarters should be 8 more than dimes, so number of quarters}=x+8\\ \\ \text{we know that the value of 1 dime is }\ 0.10 \text{ value of one quarter is }\ 0.25\\ \\ \text{And since the total value of quarters and dimes is }\ 2.80, \text{ so we have}\\ \\ 0.10(x)+0.25(x+8)=2.80\\ \\ \Rightarrow 0.10x+0.25x+2=2.80\\ \\ \Rightarrow 0.35x=2.80-2\\ \\ \Rightarrow 0.35x=0.80$

$\Rightarrow x=\frac{0.80}{0.35}=2.29\\ \\ \text{so if we take 2 dimes then we'll have to take 10 quarters according to friend.}\\ \\ \text{So the statement of friend is }$ WRONG