Question

11. Two
in the ratio 3:5
When 8 is added to each the nation
changes to 5:7 Identify the
numbers​

Answer 1

Explanation:

Two numbers are in the ratio 3:5. If 8 is added to both the numbers, the ratio becomes 2:3. What is the larger number?

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Lets call the numbers p and q (for a change)

The first ratio means 5p = 3q

This may look the wrong way round, but remember p is the smaller number so needs the bigger multiplier to become equal

The second Ratio means 3(p+8) = 2(p+8) [using the same logic)

3p + 24 = 2q + 16 [Multiplying out the brackets]

Now we have got two equations, there are different ways to combine them

I’m going to do this by substitution

Simplify the 2nd to give 3p + 8 = 2q and then q = 3/2 * p + 4

(By taking 16 from both sides then dividing by 2)

5p = 3(3/2 * p + 4) = 9/2 + p + 12 - Substituting our statement for q into the first equation)

The 1/2 is a bit awkward so I will multiply through by 2

10p = 9p + 24

Take 9p from both sides

p = 24

Use this value of p and the first ratio

3q = 5 * 24 = 120.

so q = 40

We have a solution now; p=24, q= 40. But I always like to check the answer against the question

p:q = 24:40 = 3:5 - good

Answer 2

Answer:

7:5

Explanation:

changes to 7 Anpadh 5 in that the number 57