← SSAT® Upper Level

Percent, Ratio and Arithmetic Word Problems

The topic E3n names first: arithmetic word problems, including every flavour of percent, ratio, proportion and rate the Upper Level test asks about.

5 topics · 23 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

Percent and the Percent Equation

  1. How it worksHow does the sentence part is percent of whole turn straight into an equation you can solve?
  2. Worked exampleFind 35 percent of 240 with no calculator by breaking it into 10 percent chunks.
  3. Worked exampleWalk me through finding the whole when 18 turns out to be 45 percent of it.
  4. Common mistakeWhy isn't asking what percent of 40 is 30 the same question as asking what percent of 30 is 40?
Your turneasy1 of 3
With no calculator, break it into ten percent chunks: what is 35 percent of 315?

Percent Change, Discount and Tax

  1. How it worksHow does a percent change always measure against the ORIGINAL amount rather than the new one?
  2. Worked exampleFind the final cost of a 60 dollar jacket marked down 25 percent and then taxed 8 percent.
  3. Worked exampleWalk me through the percent increase when a town grows from 250 people to 320.
  4. Common mistakeWhy isn't a 20 percent drop cancelled out by a 20 percent rise the very next day?
  5. Going furtherWhat happens to a price after three straight years of 10 percent increases stacked on each other?
Your turnmedium1 of 3
A jacket costs 96 dollars, is marked down 25 percent and is then taxed 8 percent on the reduced price. What is the final cost in dollars?

Ratios and Proportions

  1. How it worksHow does a ratio turn into parts of a whole, so that 3 to 2 becomes 3/5 and 2/5?
  2. Worked exampleFind how to split 45 marbles between two jars in a 4 to 5 ratio.
  3. Worked exampleWalk me through solving 7/12 = x/30 by cross multiplying.
  4. Common mistakeWhy doesn't adding 2 to both halves of a 3 to 5 ratio leave the ratio unchanged?
  5. Going furtherWhat changes when a ratio has three parts instead of two, like 2 to 3 to 7?
Your turneasy1 of 3
Nine times 9 marbles are split between two jars in a 4 to 5 ratio. How many go into the larger jar?

Rates, Unit Rates and Distance-Rate-Time

  1. How it worksHow does the distance equals rate times time triangle let you solve for whichever one is missing?
  2. Worked exampleFind how long a 174 mile drive takes at a steady 58 miles per hour.
  3. Worked exampleWalk me through a unit rate problem where 7 notebooks cost 10.50 in dollars.
  4. Common mistakeWhy isn't the average speed for a round trip just the average of the two speeds?
Your turneasy1 of 3
Write an expression, in terms of r, for the number of hours a 259 mile drive takes at a steady r miles per hour.

Multi-Step Arithmetic Word Problems

  1. How it worksHow does drawing the quantities as bars turn a tangled word problem into one subtraction?
  2. Worked exampleFind the change from 50 in dollars after buying three shirts priced at 12.75 each.
  3. Worked exampleWalk me through scaling a recipe written for 6 people so that it feeds 15.
  4. Worked exampleFind each person's share when a bill of 84 in dollars plus an 18 percent tip is split four ways.
  5. Common mistakeWhy doesn't the word more in a word problem always mean you should add?
Your turneasy1 of 3
A shopper pays with 71 dollars after buying three shirts priced at 13 dollars each. How much change does she get, in dollars?

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