The difference of 1/2 of one number and 2/3 of another number is equal to 2. If the first number were to decrease by 5/6 of it, and the second number was to increase by 1/6 of it, their sum would be equal to 59. Find the two numbers.
*** I have attempted this problem several times and have received crazy and impossible fractions with decimals miles long. The answer to the problem is most likely a whole number or a common fraction. Viewer discretion is advised. ***
*** It is also spring vacation for those living in the good ol' USA, so totally understand if you are too lazy to even read this over. ***
Answers
one number and 2/3 of another number is equal to 2. If the first number were to decrease by 5/6 of it, and the second number was to increase by 1/6 of it, their sum would be equal to 59. Find the two numbers.
*** I have attempted this problem several times and
Answer: The answer is 60 and 42.
Step-by-step explanation: So, the way I solved this problem was by creating a system of equations and solving it with substitution. Let’s say the first number is ‘x’ and the second number is ‘y’. I created two equations:
1/2x-2/3y=2,
And
(X-5/6x)+(y+1/6y)=59.
I then solved like this:
1/2x+(-2/3)+2/3y=2+2/3y
1/2x=2/3y+2. Divide both sides by 1/2
x=4/3y+4
The next part went like this:
1/6x+7/6y=59. Substitute 4/3y+4 for x
1/6(4/3y+4)+7/6y=59. Simplify and add (-2/3) to both sides
25/18y+2/3+(-2/3)=59+(-2/3). Simplify
25/18y=175/3. Divide both sides by 25/18
y=42
Last step is substitute 42 for y in x=4/3y+4:
x=4/3(42)+4
x=60
So, y=42, and x=60, which gives you the two numbers
But, seriously though, is this for RSM? Cause I go to RSM, and it was on my 7th grade Algebra homework this week...