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Translate to a system Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than $500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is $3 and for a package the cost is $7.

Sagot :

Given:

Let x be the number of the cards and y be the number of the package.

Given that the number of cards is at least 4 more than twice the number of packages.

[tex]x=2y+4[/tex]

Given that mailing costs no more than $500 and the cost of mailing a card is $3 and for a package, the cost is $7.

[tex]3x+7y=500[/tex]

Substitute x=2y+4 in this equation, we get

[tex]3(2y+4)+7y=500[/tex]

[tex]6y+8+7y=500[/tex]

[tex]13y=500-8[/tex]

[tex]y=\frac{492}{13}[/tex][tex]y=37.8[/tex]

Let y=37 and substitute in x=2y+4, we get

[tex]x=2\times37+4[/tex][tex]x=78[/tex]

Hence the number of cards = 78 and the number of packages =37.

The total cost for this is $493 not more than $500.

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