Erik and amanda are selling boxes of fruit for a habitat for humanity fundraiser. customers can buy small boxes of fruit and large boxes of fruit. erik sold 25 small boxes of fruit and 14 large boxes of fruit for a total of $402.00. amanda sold 21 small boxes of fruit and 12 large boxes of fruit for a total of $342.00. find the cost of one small box of fruit and the cost of one large box of fruit.

Cost of smaller box is $6.00 and cost of larger box is $18.00                          

Step-by-step explanation:

We are given the following information in the question:

Let x be the cost of small boxes and y be the cost of larger fruit boxes.

Eric sold 25 small boxes and 14 large boxes for $402.00

This can be written in the form of expression:

Amanda sold 21 small boxes and 12 large boxes for $342.00

This can be interpreted with the expression:

Now, we have two equations in two variables. Thus, solving these equations with the help of substitution method:

Solving this equation, we have x= 6.

Putting this value of x in any of the equation, we get,

Therefore, cost of smaller box is $6.00 and cost of larger box is $18.00

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step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.