Question 185845: Connect English With Mathematics
1. Translate each sentence into a an equation. Tell how you are asssigning the two variables in each.
a) John has nickels and dimes that total $2.50 in his pocket.
I need help pleaseeeeeeeeee... Answer by solver91311(17077) (Show Source):
When you have problems involving coins, or any other things that have value, you have two quantities to deal with. First is the actual number of coins, and second is the value of that number of coins. Generally, when I do coin problems, I change the total value from dollars to cents. In this case, instead of using $2.50, I would use 250 cents. That will make the coefficients in the equation that I develop for the value be integers instead of decimal fractions.
For the given problem, you know that you have some nickels and some dimes. If you use n for the number of nickels and d for the number of dimes you can say that the total value of your nickels is 5n cents and the total value of your dimes is 10d cents.
The problem tells us that the total value of the money in John's pocket is $2.50, or 250 cents, so we can write:
Because, if he only has nickels and dimes, then the value of the nickels plus the value of the dimes must equal 250 cents.
By the way, if you don't change the units from dollars to cents, then 0.05n dollars is the value of the nickels and 0.10d dollars is the value of the dimes and the equation would look like:
The solution, that is the specific values of n and d, will be the same, it is just that I think it is easier to do the arithmetic if the coefficients are integers.