(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. a) If you have 22 coins consisting only of pennies, nickels, and dimes, and the coins have a total value of 100 cents, how many pennies, nickels, and dimes do you have? Also you have the same number of nickels and dimes.

b) If you do not know that you have the same number of nickels and dimes, what is the answer to the above question?

3. The attempt at a solution

I was able to figure out the answer to the first question by making the following system of equations:

[tex]x + 5y + 10z = 100[/tex]

[tex]x + y + z = 22[/tex]

[tex]y - z = 0[/tex]

I converted this into a matrix, row reduced it, and got x=10, y=6, and z=6, in which x=penny, y=nickel, and z=dime.

However, I am unsure about part b. How can you find the number of pennies, nickels, and dimes when you have 2 equations and 3 variables? I tried, but I end up with a system of equations of:

[tex]x-\frac{5}{4}z = \frac{5}{2}[/tex]

[tex]y + \frac{9}{4}y = \frac{39}{2}[/tex]

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# Homework Help: Linear system problem

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