Question

Sierra has a total of 61 dimes and quarters in her piggy bank. She has
3 more quarters than dimes. The coins have a total value of $10.90.
How many dimes and how many quarters does she have? [Hint: Use
the decimal values of the c coins to write an equation.] Show your work.

Farenheit temperature F, can be found from a Celsius temperature, C, using formula F= 1.8C + 32. Write an equation to find the temperature at which the Farenheit and Celsius readings are equal. Then find that temperature. Show your work.

Answer 1

If the amount of quarters is x and the amount of dimes is x, we have 
x+y=61

In addition, we know that x-3=y (since there are 3 more quarters than dimes). Plugging that into x+y=61, we have x+x-3=61 and by adding 3 to both sides we get 2x=64. Dividing both sides by 2, we get x=32 quarters.

If F=C, that means that 1.8C+32=C. Subtracting C and 32 from both sides, we get 0.8C=-32. Dividing 0.8 from both sides, we get C=-32/0.8=-40