Arectangular field measures 150ft by 80ft. part of the lawn is torn up to install a walk of uniform width around it. the area of the new field is one-half the area of the old. how wide is the walk?

Half the area is 6000.
let x be the width of the walk so the inner rectangle has a length of 150-2x and width 80-2x and hence its area is (150-2x)(80-2x) which is equal to 6000.

so now we have an equation in terms of x which reduces to a quadratic and we solve for x