Solve for the unknowns in the following problem: Jamal sells cookies and lemonade for his baseball team's fundraising event. A cookie is priced at $1.25 each, and lemonade is priced at $1.00 each. Last week, Jamal sold a combined total of 45 cookies and lemonades and collected $51.75. How many of each item did Jamal sell last week? (1 point)
Let x be the number of cookies sold.
Let y be the number of lemonades sold.
The total number of cookies and lemonades sold is given as 45:
x + y = 45
The total amount collected from selling cookies and lemonades is given as $51.75:
1.25x + 1.00y = 51.75
Now, we can solve these two equations simultaneously to find the values of x and y.
From the first equation:
x = 45 - y
Substitute this into the second equation:
1.25(45 - y) + 1.00y = 51.75
56.25 - 1.25y + 1.00y = 51.75
56.25 - 0.25y = 51.75
-0.25y = -4.5
y = 18
Substitute y = 18 back into x = 45 - y:
x = 45 - 18
x = 27
Therefore, Jamal sold 27 cookies and 18 lemonades last week.