The standard basketball court for college women is twice as long as its wide.the standard basketball court for college men is 4 feet longer,5 feet wider,and 650 square feet greater in area than the womens court.find the dimensions of the men's court.
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Let m represent the subscription rate for a man, and w the subscription rate for a woman.
m/w=4/3, or m=(4/3)w.
2 men and 5 women paid 460. Thus 2m+5w=460.
Substitute (4/3)w for m, in 2m+5w=460.
This gives an equation in the unknown w. Solve for w
2(4/3)w +5w=460 or (23/3)w=460. Answer is w=60
Use this value in the relation m=(4/3)w to get m=80. Check m/w=80/60=4/3
The current area of the pond is 18m by 12 m, so, if A is the current area, A=18*12
Twice the area would be 2A and it is to be accomplished by adding the same amount, say x, to both dimensions. In symbols, that is:
2A = (18+x) * (12+x)
But we know A is 18*12, so
2(18*12) = (18+x) * (12+x) ; doing the arithmetic
432 = (18+x) * (12+x) ; doing the multiplication using FOIL (first, outside, inside, last)
432 = 18*12 + 18x +12x + x*x ; simplying
432 = 216 + 30x + x*x ; or
0 = -216 + 30x + x*x : or
x*x + 30x -216 = 0 ; using the quadratic equation (or factoring)
(x-6) (x+36) = 0
This has two solutions, 6 and (-36). Since a negative number doesn't make sense in this case, the answer is to add 6m to each side.
Check (18+6) (12+6) = ?
24 * 18 = ?
432 , which is indeed twice the original area of 216 ( = 18*12)
use simultaneous equations, with x = # of men and y = # of women:
x + y = 5000 --> convert to x = 5000 - y
1.1x + 1.15y = 5600
1.1 (5000 - y) + 1.15y = 5600
5500 - 1.1y + 1.15y = 5600
.05y = 100
y = 2000
plug y = 2000 into x + y = 5000
therefore x = 3000