Question

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?

Answer 1

the cost each of one blueberry pie is $14

and one blackberry pie is $18

Step by step explanation:

Given that;

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.

Let x represent the cost of blueberry pies and y the cost of blackberry pie.

3x + 12y = 258 ........1

4x + 3y = 110 ..........2

To solve the simultaneous equations;

Multiply equation 2 by 4, equation 2 becomes;

16x +12y = 440 .......3

Subtract equation 1 from 3;

16x-3x + 12y-12y = 440-258

13x = 182

x = 182/13 = 14

Substituting x=14 to equation 2

4(14) + 3y = 110

3y = 110 - 4(14)

3y = 54

y = 54/3

y = 18

the cost each of one blueberry pie is $14

and one blackberry pie is $18

Answer 2

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

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.