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 <em>y = 1268 - 0.6x </em>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
