Anthony has 7 bills. All the bills are tens or twenties. The bills Anthony has total $100 in value. How many of each hill does Anthony have?
Pretty sure the solving method is solving systems of equations but you have to isolate the variables and stuff.. please help!!
Let X = tens and y = twenties
X = 7 - y
10 X + 20 y = 100
Substitute 7-y for X in the second equation and solve for y, then use first equation to find x.
To solve this problem, we can set up a system of equations. Let's define two variables:
Let x represent the number of tens Anthony has.
Let y represent the number of twenties Anthony has.
Based on the information given, we can establish two equations:
Equation 1: x + y = 7 (since Anthony has a total of 7 bills)
Equation 2: 10x + 20y = 100 (since the value of the bills totals $100)
Now, we can solve the system of equations using the method of substitution or elimination.
Method 1: Substitution
From Equation 1, we can isolate x:
x = 7 - y
Substituting this value of x into Equation 2, we get:
10(7 - y) + 20y = 100
70 - 10y + 20y = 100
10y = 30
y = 3
Substituting y = 3 back into Equation 1, we find:
x + 3 = 7
x = 4
Therefore, Anthony has 4 ten-dollar bills (x=4) and 3 twenty-dollar bills (y=3).
Method 2: Elimination
Multiply Equation 1 by 10 to make the coefficients of x the same:
10(x + y) = 10(7)
10x + 10y = 70
Now, subtract Equation 2 from this equation:
(10x + 10y) - (10x + 20y) = 70 - 100
10x + 10y - 10x - 20y = -30
-10y = -30
y = 3
Substituting y = 3 back into Equation 1, we find:
x + 3 = 7
x = 4
Therefore, Anthony has 4 ten-dollar bills (x=4) and 3 twenty-dollar bills (y=3).
Both methods lead us to the same result: Anthony has 4 ten-dollar bills and 3 twenty-dollar bills.