Final answer:
Using a system of linear equations and the elimination method, we find that one small box of tangerines costs $5 and one large box costs $16. However, these findings do not match any of the provided answer choices, suggesting there may be an error in the question or the options given.
Step-by-step explanation:
To solve for the cost of one small box of tangerines and one large box of tangerines, we can create a system of linear equations based on the information provided:
Let x be the cost of a small box of tangerines and y be the cost of a large box of tangerines.
From Jessica's sales, we have the equation:
5x + 7y = 137
From Micaela's sales, we have the equation:
10x + 5y = 130
To solve the system of equations, we can use either substitution or elimination. For this example, we'll use elimination.
Multiply the first equation by 2 to allow us to eliminate x from the system:
10x + 14y = 274
Now subtract the second equation from this new equation:
(10x + 14y) - (10x + 5y) = 274 - 130
This simplifies to:
9y = 144
Divide by 9 to get the cost of one large box:
y = 16
Now substitute y = 16 into the first original equation:
5x + 7(16) = 137
This simplifies to:
5x + 112 = 137
Subtract 112 from both sides to solve for x:
5x = 25
Divide by 5 to get the cost of one small box:
x = 5
Therefore, the correct answer is that one small box of tangerines costs $5 and one large box costs $16. However, since this is not one of the given options and there might be an error in the question or the options, we cannot confidently select one of the provided choices (a, b, c, d) as correct.