Aaron earns $1.50 for every video game he sells. When he sells one carton of 30 video games, he earns an additional $10. What is the minimum number of video games he has to sell in order to earn $450?
Assuming he earns an extra $10 for each carton of 30, we have
1.50x + 10(⌊x/30⌋) >= 450
x >= 246.7
check:
240 games is 8 carton, so he gets an extra $80
80 + 1.5*246 = 449.00
the 247th game earns him another $1.50, putting him at $450.50
x is greater than or equal to 246.70
Yes
To find the minimum number of video games Aaron has to sell in order to earn $450, we need to set up an equation based on the given information.
Let's say the number of video games he needs to sell is "x".
Aaron earns $1.50 for every game he sells, so the total amount he earns from selling x games is 1.50x.
When he sells one carton of 30 video games, he earns an additional $10, so the total additional amount he earns from selling one carton is $10.
Since one carton contains 30 games, the additional amount he earns per game from selling one carton is 10/30 = $0.333.
So, the total amount he earns from selling x games PLUS one carton is 1.50x + $0.333x.
We can now set up an equation to solve for x:
1.50x + $0.333x = $450
Combining like terms, we get:
1.833x = 450
Now, divide both sides of the equation by 1.833 to isolate x:
x = 450 / 1.833
Using a calculator, the approximate value of x is 245.35.
Since we can't have a fractional or decimal number of games, we need to round up to the nearest whole number.
Therefore, the minimum number of video games Aaron has to sell to earn $450 is 246.