A jar contains n nickels and d dimes. There are 18 coins in the jar, and the total value of the coins is $1.15. How many nickels and how many dimes are in the jar? (Hint: Nickels are worth $0.05 and dimes are worth $0.10.)There are....... nickels and .....dimes in the jar.?

Accepted Solution

Answer:There are 13 nickels and 5 dimes in the jar.Step-by-step explanation:Total number of coins = 18Number of nickels =[tex]n[/tex]Number of dimes = [tex]d[/tex]Therefore [tex]n+d=18[/tex]Total value of coins = $1.15Value of [tex]n[/tex] nickels = $[tex]0.05n[/tex]Values of [tex]d[/tex] dimes = $[tex]0.10d[/tex]therefore [tex]0.05n+0.10d=1.15[/tex]We have a system of equation to solve(1) [tex]n+d=18[/tex](2) [tex]0.05n+0.10d=1.15[/tex]Multiplying equation (2) with [tex]-10[/tex][tex]-0.5n-d=-11.5[/tex]Now adding it to equation (1)        [tex]n+d=18[/tex][tex]-0.5n-d=-11.5[/tex]We get [tex]0.5n=6.5[/tex]Dividing both sides by [tex]0.5[/tex][tex]\frac{0.5n}{0.5}=\frac{6.5}{0.5}[/tex]∴ [tex]n=13[/tex]Plugging value of [tex]n[/tex] in equation (1).[tex]13+d=18[/tex]Subtracting both sides by 13.[tex]13+d-13=18-13[/tex]∴ [tex]d=5[/tex]Therefore there are 13 nickels and 5 dimes in the jar.