Unit 1 · Essential SkillsE6 · Word Problems · Ground Ops

Translate Word Problems into Math

Name the unknown, turn each relationship into an equation, and answer the quantity requested.

29 min
Unlocks: Mission Briefing Room
Desmos way

Ready when you are

7 steps · about 29 minutes

Start with the warm-up.

Start

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Warm-up

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Key terms

Variable: A symbol for an unknown quantity with stated units.
Constraint: A condition every valid solution must meet.
Fixed fee: A constant amount independent of usage.

Step 2 of 7Try it firstDone

Try it first

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Take a shot before the lesson. Write one relationship from the stem, even if you do not finish.

Step 3 of 7LearnDone

The big idea

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See the structure

Start by naming one unknown with units. Translate one relationship at a time, then check that every number in the equation has compatible units.

Key idea

Name quantities before calculating

Write what each number measures. A correct calculation with the wrong quantity or unit still misses the question.

Build a reliable method

Words signal operations: “per” often means divide, “of” often means multiply, and “is” often marks the equals sign. Read the whole relationship before committing.

Explore in Desmos

Solve a fixed-plus-variable cost

A rental costs $4 plus $6 per hour and totals $46. Graph the equation, read the solution

x=7

, and check that the fixed charge appears only once.

The calculator is live: change anything and see what happens.

Solve a fixed-plus-variable cost

Degree mode

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Stretch to a 36

The variable you solve for may not be the answer. Reread the highlighted ask, substitute back, and report the requested quantity with its unit.

Trap

A believable answer to the wrong question

The choices often include a correct intermediate number. Before selecting it, reread the highlighted ask and check the unit, sign, and domain.

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Worked examples

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Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1: Translate a fixed fee and a repeated fee

Problem

A rental costs $8 plus $6 per hour and totals $50. How many hours?

Write

8+6h=50

, then subtract 8:

6h=42

Which equation represents the fixed and repeated quantities?

Divide by 6:

h=7

Which substitution recreates the stated total?

Worked example

Example 2: Model consecutive integers symmetrically

Problem

Three consecutive integers sum to 72. What is the greatest integer?

Let the middle integer be

n

(n-1)+n+(n+1)=72

Which equation represents the fixed and repeated quantities?

3n=72

, so

n=24

and the greatest is

25

Which substitution recreates the stated total?

Faded example · you finish it

Example 3: Complete the setup and result

Problem

How many miles

m

satisfy the taxi-fare equation

4+2.50m=19

Choose the setup that follows the stated relationship.

Choose the resulting value.

Desmos way

Solve a taxi model by intersection

Graph y=4+2.5x for the fare after

x

miles and y=19 for the paid total. Click their intersection.

Read

(6,19)

, so the trip was 6 miles. Check the model directly:

4+2.5(6)=19

. Algebra is quicker here; the graph shows what the solution means.

Solve a taxi model by intersection

Degree mode

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Practice

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Spot the mistake

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Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

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Exit ticket

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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.