Find the number that must be added to the terms of the ratio 13 : 25 to make…
2022
Find the number that must be added to the terms of the ratio 13 : 25 to make it equal to 7 : 10.
Answer: C. 15 — ConceptWhen the same number x is added to both terms of a ratio a : b, the new ratio is (a + x) : (b + x). To match a target ratio m : n, write (a + x)/(b +…
- A.
8
- B.
11
- C.
15
- D.
13
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Concept
When the same number x is added to both terms of a ratio a : b, the new ratio is (a + x) : (b + x).
To match a target ratio m : n, write (a + x)/(b + x) = m/n and solve by cross-multiplication.
Application
Let x be the number added to both terms. Then (13 + x)/(25 + x) = 7/10.
Cross-multiply: 10(13 + x) = 7(25 + x).
Expand both sides: 130 + 10x = 175 + 7x.
Collect like terms: 10x - 7x = 175 - 130, so 3x = 45 and x = 15.
Cross-check
Adding 15 gives 28 : 40. Dividing both terms by 4 gives 7 : 10.
Therefore, the required number is 15.