If A+B=60 and A-B=40, what is A divided by B?

If A+B=60 and A-B=40, what is A divided by B?

Solution:

Approach 1: Elimination

1. We can eliminate B by adding the two equations together. Notice that B cancels out: (A + B) + (A – B) = 60 + 40 2A = 100 Divide both sides by 2 to isolate A: A = 50
2. Now that you know A is 50, plug it back into either of the original equations to solve for B. We’ll use the first equation: 50 + B = 60 Subtract 50 from both sides to isolate B: B = 10
3. Finally, calculate A / B: A / B = 50 / 10 = 5

Approach 2: Using the first equation to express B in terms of A

1. From the first equation, A + B = 60, we can rewrite it to express B in terms of A: B = 60 – A
2. Substitute this expression for B in the second equation, A – (60 – A) = 40. This becomes: A – 60 + A = 40 Combine like terms: 2A – 60 = 40
3. Add 60 to both sides to isolate A: 2A = 100 Divide both sides by 2 to solve for A: A = 50
4. Now that you know A is 50, plug it back into the expression for B you derived in step 1: B = 60 – 50 = 10
5. Finally, calculate A / B: A / B = 50 / 10 = 5

Therefore, using either approach, A / B is equal to 5.