A jar has some dimes and quarters in it. There are a total of 27 coins and the total value of the coins is $4.50. Melissa says there are 5 dimes and 16 quarters. Doug says there are 30 dimes and 6 quarters. Zoey says there are 20 dimes and 10 quarters. They are all incorrect. Select one person and explain why he or she is incorrect. Then, state the correct number of each type of coin. Be sure to explain how you arrived at your answer.
You must:
identify who you have chosen
explain why you think he or she is incorrect
justify your reasoning mathematically
give the correct number of each type of coin
use appropriate mathematics to support your answer
please do these questions on top also, thanks!
+592 We can choose Doug. The reason Doug is incorrect is because if there are 30 dimes and 6 quarters, they will have a total amount of 36 coins, which is not 27.
We know that a dime is worth $10$ cents, and a quarter is worth $25$ cents. Lets say that there are d dimes, and q quarters. this means that
10d+25q=450
d+q=27
we can multiply the second equation by 10:
10d+10q=270
and now we can subtract that equation from the first equation to cancel out the d and we have
25q-10q=450-270=15q=180
q=$\frac{180}{15}$=$\boxed{12}$
Now we can plug that value in for q, and we have
d+12=27
d=27-12=$\boxed{15}$
