Jessica sold 210 magazine subscriptions during a fundraiser at her school. The subscriptions either cost $23 per year or $45 for two years. Her sales totaled $6,150. How many one-year and how many two-year subscriptions did Jessica sell?
let x = # at $23, and y = # at $45.
y = 210 - x
23x + 45y = 6150
Substitute 210-x for y in the second equation and solve for x. Insert that value into the first equation to solve for y. Check by putting both values into the second equation.
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To solve this problem, we can use a system of equations. Let's say x represents the number of one-year subscriptions sold, and y represents the number of two-year subscriptions sold.
We are given the following information:
1) Jessica sold a total of 210 magazine subscriptions, so we have the equation: x + y = 210
2) The total sales amounted to $6,150, so we have the equation: 23x + 45y = 6,150
We can solve this system of equations to find the values of x and y.
1) Start by solving the first equation for x:
x + y = 210
x = 210 - y
2) Substitute the value of x in the second equation:
23x + 45y = 6,150
23(210 - y) + 45y = 6,150
4,830 - 23y + 45y = 6,150
22y = 1,320
y = 1,320 / 22
y = 60
3) Substitute the value of y back into the first equation to solve for x:
x + 60 = 210
x = 210 - 60
x = 150
Therefore, Jessica sold 150 one-year subscriptions and 60 two-year subscriptions.