Question

A boy has a lemonade stand with a cash box that has 22 coins in it. If the coins are made up of nickles and

half dollars and have a value of $5.15, how many of each coins does he have in the cash box?
He has
nickles and
half dollars.
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Answer 1

`Nickels: 13\\\\Half\ dollars:9`

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:

`\left \{ {{n+h=22} \atop {0.05n+0.5h=5.15}} \right.`

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":

`\left \{ {{-0.5n-0.5h=-11} \atop {0.05n+0.5h=5.15}} \right.\\...........................\\-0.45n=-5.85\\\\n=(-5.85)/(-0.45)\\\\n=13`

Finally, substitute the value of "n" into the first equation and solve for "h":

`13+h=22\\\\h=22-13\\\\h=9`