# Numbers at ratio

The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?

s =  25

### Step-by-step explanation:

2a=3b
3(a+5)=4(b+5)
s = a+b

2·a=3·b
3·(a+5)=4·(b+5)
s = a+b

2a-3b = 0
3a-4b = 5
a+b-s = 0

Pivot: Row 1 ↔ Row 2
3a-4b = 5
2a-3b = 0
a+b-s = 0

Row 2 - 2/3 · Row 1 → Row 2
3a-4b = 5
-0.333b = -3.333
a+b-s = 0

Row 3 - 1/3 · Row 1 → Row 3
3a-4b = 5
-0.333b = -3.333
2.333b-s = -1.667

Pivot: Row 2 ↔ Row 3
3a-4b = 5
2.333b-s = -1.667
-0.333b = -3.333

Row 3 - -0.33333333/2.33333333 · Row 2 → Row 3
3a-4b = 5
2.333b-s = -1.667
-0.143s = -3.571

s = -3.57142857/-0.14285714 = 25
b = -1.66666667+s/2.33333333 = -1.66666667+25/2.33333333 = 10
a = 5+4b/3 = 5+4 · 10/3 = 15

a = 15
b = 10
s = 25

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Showing 1 comment:
Math Student
Q: 7 : 4 = 42 : x

A: x = 42 * 4/ 7 = 24

7:4 = 42:24

Have a fun math!

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