ASVAB - Making Sense of Word Problems

ASVAB - Making Sense of Word Problems

Setting Up a Word Problem

• The goal of these word problems is to set them up into an equation that we can solve

• Your job is to dig out the relevant facts and state them in mathematical terms. You do this by:

• Getting Organized.

• Understanding the Problem.

• Identifying the information you need.

• Translate the problem into an equation you can solve.

Getting Organized

Getting organized isn’t really a step as much as it is a method. You need to be organized throughout the problem-solving process. Working clearly will help you think clearly, and it’ll ensure you don’t get lost, while trying to define and solve the problem.

Getting Organized

• Sometime drawing a picture helps.

• Problem: A ladybug walks 5 inches directly south. She then turns and walks 10 inches directly east. If she then sprouts her wings and flies directly back to her starting point, how far will she have to fly?
  

• Once you draw the picture (hopefully) you realize you can solve this by finding the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
  

•  $a^2+b^2=c^2$  

Multiple Choice

A ladybug walks 5 inches directly south. She then turns and walks 10 inches directly east. If she then sprouts her wings and flies directly back to her starting point, how far will she have to fly?

• 125 inches

• 62.5 inches

• 11.2 inches

• 15 inches

Solving the Problem

•  $a^2+b^2=c^2$  
  

• Plug in the information: $5^2+10^2=c^2$  

• Square the 5 and 10:  $25+100=c^2$  

• Simplify: $125=c^2$  

• Take square root of both sides:  $\sqrt{125}=\sqrt{c^2}$  

•  $11.18022989=c$  

• Round the answer:  $c=11.2$  

Understanding the Problem

• A word problem can be broken into TWO PARTS:

• 1 - The Problem Statement: this is the problem itself which has the information you NEED as well as "distracters" which is extra information you don't need to solve the problem.

• 2 - The Problem Question: this is what the questions is exactly asking you to find.

Multiple Select

Identifying the Information You Need:

In November, the National Weather Service recorded 1 inch of snow and 3 inches of rain in Grand Forks, North Dakota. In December, these numbers were reversed, with 3 inches of snow, and only 1 inch of rain. How much snow did Grand Forks Receive in total?

🔷🌨Which pieces of information do you NEED?🌨🔷

• 1 inch of snow

• 3 inches of rain

• 3 inches of snow

• 1 inch of rain

Identifying the Information You Need

• In November, the National Weather Service recorded 1 inch of snow and 3 inches of rain in Grand Forks, North Dakota. In December, these numbers were reversed, with 3 inches of snow, and only 1 inch of rain. How much snow did Grand Forks Receive in total?

• It's asking: How much SNOW did Grand Forks Receive in total?

• So you need the 1 inch of snow and 3 inches of snow

• The answer would be 4 inches of snow.

QUICK TIP on Identifying the Information

• Pay particular attention to include units of measure, such as feet, miles, inches, pounds, dollars, and so on.

• One of the fastest ways to mess up on a math word problem is by not seeing that the units of measure are different.

• One could be miles and the other feet

• One could be feet and the other inches

• Once could be in dollars and the other in cents

• Once could be in hours and the other in seconds

Multiple Choice

A carpenter buys 44 feet of wood. If she adds the wood to the 720 inches of wood she already owns, how many feet of wood will she have?

• 764 feet

• 1248 feet

• 528 feet

• 104 feet

Identifying the Units of Measure

• A carpenter buys 44 feet of wood. If she adds the wood to the 720 inches of wood she already owns, how many feet of wood will she have?

• The question is asking for feet so we should make all the units feet.

• 12 inches = 1 foot

• So take 720 inches ÷ 12 = 60 feet

• So it's 44 feet of wood + 60 feet of wood = 104 feet of wood.

Identifying ADDITION key words

• Added to

• Increased by

• More than

• Combined

• Together

• Total of

• Sum

Identifying SUBTRACTION key words

• Decreased by

• Minus

• Less

• Less than

• Difference between / of

• Fewer than

Identifying MULTIPLICATION key words

• Of

• Times

• Multiplied by

• Product of

• Increased by a factor of

• Decreased by a factor of

Identifying DIVISION key words

• A

• Per

• Average

• Ration of

• Quotient of

Multiple Choice

The drill sergeant can do 100 pushups more than Private Jones. Together, they can do 300 pushups. How many pushups can Private Jones do? (let J = the number of pushups Private Jones can do and let D = the number of pushups the drill sergeant can do)

💠Which equation represents the problem?💠

•  $J+100=D$  

•  $D+J=100$  

•  $D+100=J$  

Multiple Choice

The difference between Bob's pay and Becky's pay would indicate with operation?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

"the sum of 13 and y" would indicate which operation?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

"fifteen percent of x" would indicate which operation?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Select

Which word(s) mean the same as division?

Select all that apply.

• Per

• Ratio of

• Increased by a factor of

• Of

• Quotient of

Multiple Choice

"the ratio of x to 8" would indicate which operation?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

"the length of a rectangle is 45 inches more that its width" would indicate which operation?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Select

Which word(s) mean the same as multiplication?

Select all that apply.

• Product

• Ratio of

• Increased by a factor of

• Of

• Difference between

Multiple Choice

Which algebraic expression represents: 'the sum of x and 15'?

• $x+15$

• $15x$
  

• $15-x$
  

• $\frac{15}{x}$
  

• $15\left(x\right)$

Multiple Select

'The product of 12 and a number k'
Select all correct expressions.

•  $12\times k$  

•  $k-12$  
  

•  $12k$  
  

•  $12\left(k\right)$  
  

•  $12+k$  

Multiple Choice

Which algebraic expression represents: 's increased by 3'?

• $s-3$

• $3s$
  

• $s+3$
  

• $\frac{s}{3}$
  

Multiple Choice

Which algebraic expression represents: 'the product of 6 and y'?

• $6+y$

• $6y$
  

• $y-6$
  

• $\frac{y}{6}$
  

Multiple Choice

Write an algebraic expression for:

14 decreased by a number

• $14+n$
  

• $14-n$
  

• $n-14$
  

• $14n$