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Age and Money

Part of the Fundamentals section of Coddy's Algebra journey. Lesson 50 of 61.

"Three times Ana's age, plus 2, is 20. How old is Ana?" Name the unknown. Let $a$ be Ana's age. Three times her age is $3a$ . Plus 2 gives $3a+2$ . The sentence says that equals 20:

$3a+2 = 20$

Subtract 2 from both sides, then divide by 3, and you get $a = 6$ . Check against the sentence. Three times 6 is 18, and 18 plus 2 is 20. Ana is 6.

Money problems work the same way. Three identical coins and 2 dollars have a total value of 20 dollars. Let $c$ be the value of one coin in dollars. Then the total gives the equation $3c+2 = 20$ . Solving gives $c = 6$ . Check that $3\cdot 6+2 = 20$ .

Challenge

Medium

Twice Ben's age, plus 7, is 31, so $2a+7 = 31$ . Solve for $a$ , Ben's age.

Try it yourself

2a+7 = 31

Get $a$ alone

All lessons in Fundamentals

1What an Equation Is

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4Two-Step Equations

Two Layers to Undo Subtract, Then Divide Add, Then Divide A Division Inside Negatives in Two Steps Recap: Two-Step Equations

7Fractions in Equations

A Fraction Coefficient Clearing One Denominator Two Denominators A Fraction Around a Sum Cross-Multiplying Recap: Fractions

10From Words to Equations

Phrases into Expressions Sentences into Equations Consecutive NumbersAge and MoneyA Perimeter Problem Recap: Words

3Negative Numbers

Below Zero A Negative Answer Negative Coefficients The Opposite of x Recap: Negatives

6Variables on Both Sides

x on Both Sides Gathering the x's Numbers and x's Everywhere Parentheses on One Side When x Is Negative Recap: Both Sides

9Special Cases

No Solution Always True Checking a Solution Recap: Special Cases

12Final Challenges

Parentheses on Both Sides Fractions and x's Decimals on Both Sides The Story Problem