Step 1: Understand (Glance Read Jot)
This Algebraic Translation problem asks you to solve for the number of members in the senate. Information is given about Republicans and Democrats in the senate this year and last year. Working Backwards may be possible because the answer choices represent a simple value (i.e., the total members) and are integers, making them relatively easy to work with.
Jot down the given information.
Last year: 20 more R’s than D’s
This year: 2 fewer R’s than last year, R’s = 23 Total
Total?
Step 2: Plan (Reflect Organize)
As you consider whether to work backwards, think about whether the answer choices (the total number of members) would be easy to plug into the given information. Since the total number of members is the same both years, working backwards will be a good strategy.
Alternatively, you could translate the given information into equations and solve.
Step 3: Solve (Do the Work)
Work Backwards
Start with answer choice (B). Plug in 36 for the total number of members, and solve for the Republicans each year.
This Year
If there are 36 total members, 36(23) = 24 Republicans this year.
Last Year
Last year, there were 2 more Republicans, meaning there were 26 Republicans.
If there were 26 Republicans last year, there were 36 −26 = 10 Democrats.
The difference between the Republicans and Democrats is 26 − 10 = 16. But according to the problem, this difference should be 20. Since the difference is too small, test a larger answer.
Test answer choice (D).
This Year
If there are 45 total members, 45(23) = 30 Republicans this year.
Last Year
Last year, there were 2 more Republicans, meaning there were 32 Republicans.
If there were 32 Republicans last year, there were 45 −32 = 13 Democrats.
The difference between the Republicans and Democrats is 32 − 13 = 19. But according to the problem, this difference should be 20. Since the difference is still too small, select the only larger answer.
Algebra
For the algebraic solution, please see
the Official Guide.
The correct answer is (E).
Hit Kudos, if it is useful.