Someone help me please

Question

Dave Bowers collects U.S. gold coins. He has a collection of

49

coins. Some are​ $10 coins, and the rest are​ $20 coins. If the face value of the coins is

​$690​,

how many of each denomination does he​ have?

Answer 1

Alrighty! Before we begin, let us translate the information the question gave us into usable equations!

Let X = number of $10 coins

Let Y = number of $20 coins

1) Let X + Y = 49 (since there are 49 total coins)

2) 10X + 20Y = 690 (the total amount of money from these coins)

This is where it gets tricky- right now we have 2 variables (X and Y), but to solve this question, we can only use 1 variable (let's choose X).

X = 49 - Y (changed from equation 1)

We plug this in for X in equation 2:

10 (49 - Y) + 20Y = 690

490 - 10Y + 20Y = 690

490 + 10Y = 690

10Y = 690 - 490 = 200

Y = 200/10 = 20

X = 49 - 20 = 29.

Thus, Dave Bowers has 29 ($10 coins) and 20 ($20 coins). Hope this helps!! :)