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elmo makes n sandwiches for a fundraiser. for each sandwich he uses b globs of peanut butter at 4 cents per glob and j blobs of jam at 5 cents per blob. the cost of the peanut butter and jam to make all the sandwiches is $2.53. assume that b, j, and n are positive integers with n>1. what is the cost, in dollars, of the jam elmo uses to make the sandwiches?

Respuesta :

MrRoyal

The cost in dollar that Elmo used to make one sandwich is $0.23, while he spent $2.53 on all the sandwiches.

Given that:

  • He used b globs at 4 cent per glob for the peanut butter
  • He used j blobs at 4 cent per blob for the jam
  • And he made a total of n sandwiches

The equation of the n sandwiches made is represented as:

[tex]n \times (4b + 5j)=\$2.53[/tex]

Express $2.53 as cents

[tex]n \times (4b + 5j)=253[/tex]

The factors of 253 are 1, 11, 23, 253.

Given that n > 1, then the value of n can either be 11 or 23

Assume n = 11, then the equation becomes

[tex]11 \times (4b + 5j)=253[/tex]

Divide both sides by 11

[tex]4b + 5j=23[/tex]

The possible values of b and j that make the above equation to be true are:

b =2 and j = 3

This is proved as follows:

[tex]4 \times 2 + 5 \times 3=23[/tex]

[tex]8 +15=23[/tex]

[tex]23 = 23[/tex]

Hence, the cost in dollar that Elmo used to make one sandwich is $0.23, while he spent $2.53 on all the sandwiches.

Read more about linear equations at:

https://brainly.com/question/14323743

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