A boy has a lemonade stand with a cash box that has 22 coins in it. If the coins are made up of nickles andhalf dollars and have a value of $5.15, how many of each coins does he have in the cash box?He hasnickles andhalf dollars.Submit Question

Accepted Solution

Answer: [tex]Nickels: 13\\\\Half\ dollars:9[/tex]Step-by-step explanation: Let be "n" the number of nickels the boy has in the cash box and "h" the number of half dollars the boy has in the cash box. Set up a system of equations: [tex]\left \{ {{n+h=22} \atop {0.05n+0.5h=5.15}} \right.[/tex] You can use the Elimination method to solve the system. Multiply the first equation by -0.5, add both equations and then solve for "n": [tex]\left \{ {{-0.5n-0.5h=-11} \atop {0.05n+0.5h=5.15}} \right.\\...........................\\-0.45n=-5.85\\\\n=\frac{-5.85}{-0.45}\\\\n=13[/tex] Finally, substitute the value of "n" into the first equation and solve for "h": [tex]13+h=22\\\\h=22-13\\\\h=9[/tex]