What is 2 numbers you can put together to get 75,000, and multiply the smaller number by 4 and add the bigger number and get 153,000?
What is 2 numbers you can put together to get 75,000, and multiply the smaller number by 4 and add the bigger number and get 153,000?
Let the smaller number=x
Let the bigger number=y
x + y=75,000
4x* + y=153,000
Solve the following system:
{x+y = 75000 | (equation 1)
4 x+y = 153000 | (equation 2)
Swap equation 1 with equation 2:
{4 x+y = 153000 | (equation 1)
x+y = 75000 | (equation 2)
Subtract 1/4 × (equation 1) from equation 2:
{4 x+y = 153000 | (equation 1)
0 x+(3 y)/4 = 36750 | (equation 2)
Multiply equation 2 by 4/3:
{4 x+y = 153000 | (equation 1)
0 x+y = 49000 | (equation 2)
Subtract equation 2 from equation 1:
{4 x+0 y = 104000 | (equation 1)
0 x+y = 49000 | (equation 2)
Divide equation 1 by 4:
{x+0 y = 26000 | (equation 1)
0 x+y = 49000 | (equation 2)
Collect results:
Answer: |
| {x = 26000
y = 49000
If i were you i would try using simeltaneous equations;
lets designate the smaller number as X
and the larger number as Y
using this all the equations you can get are;
X + Y = 75000 (lets call this equation A)
4X + Y = 153000 (lets call this equation B
cool? - anyway now we have to get rid of one of the unknowns
Equation A - Equation B should do it (notice the presence of a singe Y in each one)
(X - 4X) + (Y - Y) = (153000 - 75000)
the Ys cancel so we get
3X = 78000
X = 26000
now we have X, Y is easy - you just put the value of X into any of the equations
soooo;
26000 + Y = 75000
Y = 75000 - 26000
Y = 49000
i didn't use a calculator, so the actual values may be off
nonetheless the meathod is solid
ta!
