Question 1124209: two numbers are in the ratio 2:5. if their difference is 48,what is the bigger number? Found 3 solutions by htmentor, Theo, MathTherapy:Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website! [Ratio is 2:5] x/y = 2/5 -> x = (2/5)y
[Difference is 48] y - (2/5)y = 48 -> (3/5)y = 48 -> y = 80
let the numbers be A and B.
let the ratio be A:B = 2:5
this can also be written at A/B = 2/5
solve for A to get A = 2/5 * B
this makes B the larger number.
therefore B - A = 48
solve for B to get B = A + 48
you have A = 2/5 * B and you have B = A + 48
replace B in the first equation with its equivalent value of A + 48 from the second equation to get:
A = 2/5 * B becomes A = 2/5 * (A + 48)
simplify to get A = 2/5 * A + 2/5 * 48
subtract 2/5 * A from both sides of this equation to get:
A - 2/5 * A = 2/5 * 48
combine like terms to get 3/5 * A = 2/5 * 48
multiply both sides of this equation by 5/3 to get:
5/3 * 3/5 * A = 5/3 * 2/5 * 48
simplify to get:
A = 10/15 * 48
solve for A to get A = 32
you have A = 32 and B = 80
B = A + 48 gets you B = 32 + 48 = 80
A/B = 2/5 becomes 32/80 = 2/5
divide 32 by 16 to get 2 and divide 80 by 16 to get 5.
this means that 32/80 is equivalent to 2/5 which means the ratio of A/B is correct.
you could also confirm by cross multiplying.
cross multiply 2/5 = 32/80 to get 160 = 160, confirming the ratios are equivalent.
Let the multiplicative factor be x
Then the numbers are: 2x and 5x
Since their difference is 48, then we get: 5x - 2x = 48
3x = 48
Larger number:
That's ALL!!