1. The present ages of a husband and wife are in the ratio of seven to six and five years ago the ratio was six to five. Find their ages now.
2. The numerator and the denominator of a fraction are thirteen and fifty, respectively. When a certain number is added to this numerator and subtracted from this denominator, the resulting fraction has a numerator to denominator ratio of two to one. Find the number.
2007-07-03 16:04:48 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
1. Husband's age: x
Wife's age: y
x/y = 7/6
6x = 7y
y = 6x/7
(x-5)/(y-5) = 6/5
5(x-5) = 6(y-5)
5x - 25 = 6y - 30
5x - 25 = 6*6x/7 - 30
5x - 25 = 36x/7 - 30
35x - 175 = 36x - 210
x = 35
y = 30
The husband is 35 and the wife is 30.
2. Fraction: 13/50
(13+x)/(50-x) = 2/1
Cross-multiply
13+x = 2(50-x)
13+x = 100-2x
3x = 87
x = 29
2007-07-03 16:18:47 · answer #1 · answered by gudspeling 7 · 0⤊ 0⤋
1. The husband and wife are currently 35 and 30 (7 to 6). 5 years ago they were 30 and 25 (6 to 5)
2. The number is 29. Since the numerator goes up as the denominator goes down, the sum of them is always going to be 63. To get them in a ratio of 2 to 1, 2/3 of 63 (which is 42) is on top, and 1/3 of 63 (which is 21) is on bottom. 42/21=2
2007-07-03 23:15:28 · answer #2 · answered by bdf1215 1 · 0⤊ 0⤋
1. The present ages of a husband and wife are in the ratio of seven to six and five years ago the ratio was six to five. Find their ages now.
6h=7w
5(h-5)=6(w-5)
5h-25=6w-30
5h=6w-5
h=6w/5-1
6h=7w substitute 6w/5-1 for h
6(6w/5-1)=7w
36w/5-6=7w
36w/5-35w/5=6
w/5=6
w=30
h=6w/5-1
h=6*30/5-1
h=35
husband is 35, wife is 30
2. The numerator and the denominator of a fraction are thirteen and fifty, respectively. When a certain number is added to this numerator and subtracted from this denominator, the resulting fraction has a numerator to denominator ratio of two to one. Find the number.
13/50
(13+x)/(50-x)=2
13+x=2(50-x)
13+x=100-2x
3x=87
x=29
check
(13+29)/(50-29)=42/21=2
2007-07-03 23:12:31 · answer #3 · answered by yupchagee 7 · 0⤊ 0⤋
1.
h/w = 7/6
(h - 5)/(w - 5) = 6/5
5h - 25 = 6w - 30
5(7/6)w + 5 = 6w
35w + 30 = 36w
w = 30
h = 35
30/25 = 6 / 5
2.
(13 + x)/(50 - x) = 2/1 = 2
13 + x = 100 - 2x
3x = 87
x = 29
42/21 = 2
2007-07-03 23:20:03 · answer #4 · answered by Helmut 7 · 0⤊ 0⤋
H/W = 7/6; (H-5)/(W-5) = 6/5
H = 7 W/6
(7W/6 - 5)/(W-5) = 6/5
(7W - 30)= 36/5 * (W-5)
35 W - 150 = 36 W - 180
w = 30: wife
H = 35: Husband
2.
( 13+X)/(50 -X) = 2/1
13+X = 100 - 2X
3X = (100-13) = 87
X = 29
2007-07-03 23:22:35 · answer #5 · answered by telsaar 4 · 0⤊ 0⤋