21.The ages of A and B are in the ratio 5: 3. After 6 years, their ages will be in the ratio 7:5. The sum of their present ages is.........................
A) 9 years
(B) 10 years
(C) 15 years
(D) 24 years
SOME ONE PLEASE GIVE ME THE CORRECT ANSWER WITH CORRECT EXPLANATION.I WILL MARK THE BEST ANSWER THE BRAINLIEST. HELP.... HELP....
Answers
Answer:
15 years
Step-by-step explanation:
The ages of A and B are in the ratio 5:3. After 6 years their ages will be in the ratio 7:5. What is the present age of A?
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A:B = 5:3
This can also be expressed as a fraction, when the given values are reduced (for example, 21/15):
A/B = 5/3
You can solve for either A or B here, but let’s solve for A
First, multiply both sides by B:
A = (5b)/3
In the second equation, A and B both increase by 6:
(A+6)/(B+6) = 7:5
recall that A = 5b/3
So substitute for A in the first equation:
((5b/3)+6)/(B+6) = 7:5
Multiply both sides by (b+6) to get rid of the denominator
((5b/3)+6) = (7(B+6)/5
Now, expand the parentheses on the right side:
((5b/3)+6)=(7b+42)/5
Drop the parentheses on the left side
(5b/3)+6 = (7b+42)/5
Multiply both sides by 15 to get rid of both denominators
15(5b/3)+15*6 = 15(7b+42)/5
(75b/3)+15*6 = 3(7b+42)
Use FOIL on the right side:
(75b/3)+15*6 = 21b+126
25b + 90 = 21b + 126
Subtract 21b from both sides, then subtract 90 from both sides:
4b = 36
Divide by 4:
b = 9
Now go back to the very first equation and pop in 9 for b:
A:B = 5:3
b = 9
A/9 = 5/3
Multiply both sides by 9:
A = 45/3
A = 15
Now go back to the second equation from the question and substitute and see if it fits:
(A+6)/(B+6) = 7/5
(15+6)/(9+6)=7/5
21/15 = 7/5
7/5 = 7/5
So the ages are 15 and 9.
Let the rationale between ages of A and B be x
The ages of A and B are in the ratio 5 : 3. Hence their age, A's present age 5x and B's present age 3x
After 6 years their ages will be in the ratio 7:5
After 6 years their ages will be A's age 5x + 6 and Bs age 3x + 6. The ratio of ages will be
5x + 6 / 3x + 6 = 7 / 5
Cross multiplication
5 ( 5x + 6) = 7 ( 3x + 6 )
25x + 30 = 21x + 42
25x - 21x = 42 - 30
4x = 12
x = 12/4
x = 3
The rationale is 3. Hence the ages
A's present age = 5x = 5 × 3= 15 years
B's present age = 3x = 3 × 3= 9 years
Answer A's present age is 15 years