Question

a) Two numbers are in the ratio 4:5. When 6 is added to each term, their ratio becomes 5:6. Find the numbers.

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Answer 1

Answer:

leta/b=4/5 call this #1; then

(a+6)/(b+6)=13/16 call this #2

from #1 a/b=4/5 multiply each side by b

a=4b/5 now substitute into #2 we get:

(4b/5+6)/(b+6)=13/16

{(4b+30)/5}/(b+6)=13/16 multiply both sides by 5

(4b+30)/b+6)=13x5/16=65/16 multiply each side by 16

16(4b+30)/(b+6)=65

(64b+480)/(b+6)=65 multiply each side by (b+6)

64b+480= 65(b+6)

64b+480= 65b+390 now subtract 64b+390 from each side

90= b

since a=4b/5 =4x90/5 =72

Answer 2

Step-by-step explanation:

{ 4x +6 }/ { 5x +6 } = 5/6

24x +36 =25x + 30

x = 6

4x = 4× 6 = 24

5x = 5×6 = 30