Quarters weigh 6 grams while dimes weigh 2 grams.

Question

Quarters weigh $6$ grams while dimes weigh $2$ grams. Tiffany has $\$5.35$ worth of quarters and dimes in her pocket weighing a total of $124$ grams. How many quarters does Tiffany have?

Answer 1

Let us call $Q$ the number of quarters and $D$ the number of dimes. So, the amount of money (in cents) gives $$25 Q+ 10 D=535$$ For the weight $$6Q+2D=124$$ So, two equations for two unknowns.

I am sure that you can take from here.

Answer 2

Start with a wild guess. Try all dimes, and fill out with quarters. 51 dimes and 1 quarter gives the right amount of money, but weighs 102+6=108 grams.

Now observe that you can replace 5 dimes with 2 quarters, maintaining the same amount of money, but adding 2 grams of weight. We still need to add 16 grams of weight, so we need to take away 40 dimes and add 16 quarters to our initial guess.

So 11 dimes and 17 quarters.