SAT Ratios, Rates, Proportions, and Units study notes

Ratios compare parts in a fixed order. Name the parts before writing the fraction, then use a scale factor. If something is added to only one part, the old and new ratios are different equations; do not scale the total blindly.

Worked example

Red and blue beads start in a 3:5 ratio. Add 12 red beads and the ratio becomes 3:4. How many beads were there first?

Write the original counts as 3k and 5k. Then (3k + 12)/(5k) = 3/4, giving k = 16. The original total is 8k = 128 beads.

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