Conceptually: With ratio problems, it's often faster to think conceptually than to do the algebra.
Target question:
What is the ratio of c to d?
If we get a
proportional relationship between the two, we'll have sufficient information.
Proportional relationships are always
multiplicative (involving multiplication or division):
"one half of something" --> (1/2)n
"5 times something" --> 5y
"25% of something" --> 0.25x
"the ratio of c to d" --> c/d
Additive relationships, on the other hand, give us information about real values, but not about proportions.
"4 more than x" --> x + 4
"10 less than y" --> y - 10
1) The ratio of 3c to 3d is 3 to 4
Multiplying each term by 3 will not change the proportion between them. The ratio of c/d will be the same as the ratio of 3c/3d.
2) The ratio c+3 to d+3 is 4 to 5
Knowing the proportional relationship after we've added real values to c and d wouldn't help. We don't know how much difference the +3 made proportionally.
Try testing numbers:
c + 3 = 4 and d + 3 = 5
c = 1, d = 2
c/d = 1/2
or...
c + 3 = 400 and d + 3 = 500
c = 397, d = 497
c/d = 397/497
That gives us a different ratio, and one that's really close to 4/5. The bigger the numbers get, the less of a difference the +3 made to the overall ratio.
To your question:
My question is if stmt 2 said c+3 to d+3 is 5 to 5 does the answer change?
We can see conceptually that that would work. No matter what numbers we might test, we'll get that c and d are equal, so the ratio must be 1/1.
Does that help?
