In Canada, $1 and $2 bills have been replaced by coins. When Marissa returned home from to San Francisco from a trip to Vancouver, she found that she had acquired 37 of these coins with a total value of $51 Canadian. How many each denomination did she have?
37 @ $1 = $37
so, there are $14 extra.
That means there were 14 $2 and 23 $1 coins.
To solve this problem, we can set up a system of equations. Let's assume that Marissa has x coins of $1 denomination, and y coins of $2 denomination.
Given that Marissa has acquired 37 coins, we can write the equation:
x + y = 37
We also know that the total value of the coins is $51 Canadian, which we can express as another equation:
1x + 2y = 51
Now, we can solve this system of equations to find the values of x and y.
We can start by solving the first equation for x:
x = 37 - y
Substituting this value of x in the second equation, we have:
1(37 - y) + 2y = 51
Expanding the equation, we get:
37 - y + 2y = 51
37 + y = 51
Subtracting 37 from both sides of the equation, we have:
y = 51 - 37
y = 14
Now, substitute this value of y back into the first equation to solve for x:
x + 14 = 37
x = 37 - 14
x = 23
Therefore, Marissa has 23 $1 coins and 14 $2 coins.