A builder is planning to build houses on a 9000m^2 plot of land. Some of the houses will be small. The others will be large. The number of small houses is represented by S. The number of large houses are represented by L. The authorities insist that there must be more small houses than large houses, and there must be at least 6 large houses.

a) write down two algebraic inequalities for these two conditions

Answer...............................and................................

Each small house requires 300m^2 of land and each large house requires 500m^2 of land .

I think the answers are: L is greater than or equal to 3000m^2 (first condition, since there must be at least 6 large houses) and 6L + S less than or equal to 9000m^2 (second condition) Is this correct?

b) use the fact that the plot of land has a total area of 9000m^2 to show that 3S + 5L is less than or equal to _< 90

but 3S = 3 X 300 = 900 and 5L 5 x 500 = 2500. we have a total of 3400. so how can 3400 be less than or equal to 90?