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BAKE SALE Cassandra and Alberto are selling pies for a fundraiser. Cassandra sold 3 small pies and 14 large pies for a total of $203. Alberto sold 11 small pies and 11 large pies for a total of $220. Determine the cost of each pie.

Sagot :

Answer:

Large pie = 13

small pie = 7

Step-by-step explanation:

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CintiaSalazar

Taking into account the definition of a system of linear equations, the cost of each small pie is $7, while the cost of each large pie is $13.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

  • x: cost of each small pie
  • y: cost of each large pie

Cassandra sold 3 small pies and 14 large pies for a total of $203. This is represented by: 3x + 14y= 203

Alberto sold 11 small pies and 11 large pies for a total of $220. This is represented by: 11x + 11y= 220

So, the system of equations to solve is:

[tex]\left \{ {{3x+14y=203} \atop {11x+11y=220}} \right.[/tex]

There are various methods to solve a system of equations, it is decided to solve by the substitution method, which consists of solving one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable y from the first equation, you obtain:

14y= 203 - 3x

y= (203 - 3x) ÷14

y= 14.5 - [tex]\frac{3}{14}[/tex]x

Replacing this expression in the second equation and solving, you obtain:

11x + 11×(14.5 - [tex]\frac{3}{14}[/tex]x)= 220

11x + 11×14.5 - 11×[tex]\frac{3}{14}[/tex]x= 220

11x + 159.5 - [tex]\frac{33}{14}[/tex]x=220

11x - [tex]\frac{33}{14}[/tex]x=220 - 159.5

[tex]\frac{121}{14}[/tex]x= 60.5

x= 60.5÷ [tex]\frac{121}{14}[/tex]

x= 7

Finally, to obtain the value of y, it is replaced in the expression previously obtained for y:

y= 14.5 - [tex]\frac{3}{14}[/tex]x

y= 14.5 - [tex]\frac{3}{14}[/tex]×7

y= 14.5 - [tex]\frac{3}{2}[/tex]

y= 13

Finally, remembering that x represents the cost of each small pie and y represents the cost of each large pie, so the cost of each small pie is $7, while the cost of each large pie is $13.

Learn more about system of equations:

https://brainly.com/question/1995493

https://brainly.com/question/3291576

https://brainly.com/question/7487907?referrer=searchResults

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