Question Help
One issue of a journal has 3 full-page ads and 5 half-page ads, generating $6340 in advertising
revenue. The next issue has 4 full-page ads and 4 half-page ads, resulting in advertising revenue
of $6625. Determine the advertising rates in this journal for full-page and half-page ads.

Step-by-step explanation:

We assume that the advertising rates in this journal for full-page ads is x ($/ad); the rate for half-page ads is y ($/ad).

The revenue for 3 full page ads are: 3x ($)

The revenue for 5 half page ads are: 5y ($)

One issue of a journal has 3 full-page ads and 5 half-page ads, generating $6340.

=> The total revenue for 3 full page and 5 half page ads are $6340

=> 3x + 5y = 6340

The revenue for 4 full page ads are: 4x ($)

The revenue for 4 half page ads are: 4y ($)

One issue of a journal has 4 full-page ads and 4 half-page ads, generating $6625.

=> The total revenue for 4 full page and 4 half page ads are $6625

=> 4x + 4y = 6625 (1)

We have:

+) 3x + 5y = 6340

=> 5y = 6340 - 3x

=> y = (6340 - 3x)/5 = 1268 - 0.6x

Replace y = 1268 - 0.6x into (1), we have:

4x + 4y = 6625

⇔4x + 4(1268 - 0.6x) = 6625

⇔ 4x + 5072 - 2.4x = 6625

⇔ 1.6x = 1553

⇔ x = 1553/1.6 = 970.625

=> y = 1268 - 0.6x = 1268 - 0.6*970.625= 1268 - 582.375 = 685.625

So the advertising rate for full page ads is $970.625, for half-page ads is $685.625