Dear Math Central: Please help with the
Two for Two
Two numbers have a ratio of 5:3. The larger number is 36 more than half
the difference of the two numbers. What are the two numbers?
NOTE: There are two pairs of numbers that will make this
a true statement. You need to find both of them. Your explanation must
use algebra (variables and equations) to communicate the method you've
used to solve the 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!
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,
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