SOLUTION: I built a swimming pool that has an area of 540 square yards. The length is 1 2/3 times the amount of the width. What could be the dimensions of the pool?

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: I built a swimming pool that has an area of 540 square yards. The length is 1 2/3 times the amount of the width. What could be the dimensions of the pool?      Log On


   

Question 963081: I built a swimming pool that has an area of 540 square yards. The length is 1 2/3 times the amount of the width. What could be the dimensions of the pool?
Answer by justlikemath(2) About Me  (Show Source):
You can put this solution on YOUR website!
given: area=540sq.yd ; +L=%281+%26+2%2F3%29%2Aw+
+A=L%2AW+
substitute values
+540=%281+%26+2%2F3%29%2Aw%2Aw+
+540=%281+%26+2%2F3%29w%5E2+
i changed the mixed fraction to improper so that it would be easy to multiply and divide
+540=%285%2F3%29w%5E2+
multiply both sides by 3 so that 3 in the denominator would be eliminated
+3%28540%29=%28%285%2F3%29w%5E2%293+
+1620=5w%5E2+
divide both sides by 5 so that 5 would be eliminated and w^2 would remain
+1620%2F5=%285w%5E2%29%2F5+
+324=w%5E2+
square both sides so that only w would remain
+sqrt%28324%29=sqrt%28w%5E2%29+
+18=w+
we already have the width=18
substitute to formula
+A=L%2AW+
+540=L%2A18+
+540=18L+
+540%2F18=%2818L%29%2F18+
+30=L+
therefore 30yards x 18yards is the dimension of the swimming pool