Final answer:
The cost of a small box of grapefruits is $4, and the cost of a large box of grapefruits is $6. This was determined by setting up a system of equations based on Maria and Darryl's sales and solving for the unknown prices.
Step-by-step explanation:
We are given two systems of equations based on Maria and Darryl's sales of grapefruit boxes for a school fundraiser. To find the cost of each different size of grapefruit box, we can set up the following equations: Let 's' be the price of a small box of grapefruits, and 'l' be the price of a large box of grapefruits. Maria: 4s + 6l = $52, Darryl: 1s + 12l = $76. Now we'll solve these equations simultaneously to find the values of 's' and 'l'. Step 1: Multiply the second equation by 4 to balance it with the first equation regarding 's'. 4(1s + 12l) = 4($76), 4s + 48l = $304. Step 2: Subtract the first equation from this new equation. (4s + 48l) - (4s + 6l) = $304 - $52, 42l = $252. Step 3: Divide by 42 to find the price of one large box. l = $252 / 42, l = $6. Step 4: Substitute 'l' back into the first equation to find 's'. 4s + 6($6) = $52,4s + $36 = $52, 4s = $52 - $36, 4s = $16, s = $16 / 4,s = $4. The cost of a small box of grapefruits is $4, and the cost of a large box of grapefruits is $6.