10) Beth and Ming are selling pies for a school fundraiser. Customers can buy blueberry pies and

blackberry pies. Beth sold 3 blueberry pies and 12 blackberry pies for a total of $258. Ming sold

4 blueberry pies and 3 blackberry pies for a total of $110. What is the cost each of one blueberry

pie and one blackberry pie?

Each blueberry pie costs $14 and each blackberry pie costs $18.

Step-by-step explanation:

If X is the price of a blueberry pie and Y is the price of a blackberry pie we have that:

3*X + 12*Y = $258

4*X + 3*Y = $110

We have a system of equations, to solve it first we can isolate one of the variables in one of the equations, let's isolate X in the first equation.

3*X = $258 - 12*Y

X = $258/3 - (12*Y)/3 = 86  - 4*Y

now we can replace it in the second equation and get:

4*(86 - 4*Y) + 3*Y = 110

344 - 16Y + 3Y = 110

344 - 13Y = 110

13Y = 344 - 110 = 234

Y = 234/13 = 18

So each blackberry pie costs $18.

And we can replace it in the equation for X and get the value of X.

X = 86 - 4*Y = 86 - 4*18 = 14

So the price of a blueberry pie is $14.

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