Question

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.

Answer 1

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.

`x=2y+4`

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.

`3x+7y=500`

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

`3(2y+4)+7y=500`

`6y+8+7y=500`

`13y=500-8`

`y=(492)/(13)`
`y=37.8`

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

`x=2*37+4`
`x=78`

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

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