Final answer:
Keshawn needs to sell 0 lollipops and 90 candy bars to raise $180 on his own
Step-by-step explanation:
In order to find out how many lollipops and candy bars Keshawn needs to sell, we can use a system of equations. Let's say he sells x lollipops and y candy bars. Since the lollipops are $2 each and the candy bars are $4 each, we can set up the equation 2x + 4y = 180 to represent the total amount he wants to raise. Now, we also know that he wants to sell these items on his own, so we can set up another equation, x + y = 0. This equation represents the total number of items he sells.
We can solve this system of equations using substitution or elimination. I'll use elimination here. Multiply the second equation by 2 to make the coefficients of x in both equations equal:
2x + 2y = 0
Now, subtract the second equation from the first:
(2x + 4y) - (2x + 2y) = 180 - 0
2y = 180
y = 90
Substitute the value of y back into the second equation to find x:
x + 90 = 0
x = -90
Since we can't have negative quantities, we discard the negative solution for x. Therefore, Keshawn needs to sell 0 lollipops and 90 candy bars to raise $180 on his own.