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James bought 22 candy bars for $137. If the king size candy bars cost $8 and a regular size candy bar cost $5 , how many of each candy bar did he buy? One equation looks like: x + y= 22 Find the other equation and solve the system.

Respuesta :

Given:

James bought 22 candy bars for $137.

If the king size candy bars cost $8 and a regular size candy bar cost $5.

To find:

The system of equation and solution of it.

Solution:

Let x be the number of king size candy and y be the number of regular size candy.

Quantity: [tex]x+y=22[/tex]           ...(i)

Cost : [tex]8x+5y=137[/tex]        ...(ii)

Multiply the equation (i) by 5.

[tex]5x+5y=110[/tex]           ...(iii)

Subtract (iii) from (ii).

[tex]8x+5y-5x-5y=137-110[/tex]

[tex]3x=27[/tex]

[tex]x=9[/tex]

Put x=9 in (i).

[tex]9+y=22[/tex]

[tex]y=22-9[/tex]

[tex]y=13[/tex]

Therefore, number of king size candy is 9 and number of regular size candy  is 13.

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