Dear Math Central: Please help with the
following problem....
Thank you for your assistance. I am the parent of a honors algebra student, taking 9th grade algebra. - Warm regards for a Happy New Year!
Hi, Since there are two numbers to be found, and you are to use algebra, I would let one of the numbers be x and the other y. You are given two facts. **Two numbers have a ratio of 5:3.**- This means that x:y as 5:3. In other words x/y = 5/3
**The larger number is 36 more than half the difference of the two numbers.**- You need to read this carefully and build an equation,
step by step. Since x/y = 5/3, x is larger than y. Thus the larger number,
x, is 36 more than...[x = 36 + ...]
half the ... [ x = 36 + 1/2...] difference between the two numbers. This could be x-y or y-x, and that is why there are two pairs of numbers.Thus x = 36 + 1/2(x-y) or x = 32 + 1/2(y-x)
Hence for the first pair you need to solve the system of equations x/y = 5/3 and x = 36 + 1/2(x-y) and for the second pair the system of equations is x/y = 5/3 and x = 36 + 1/2(y-x). I hope this helps, Penny |