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Flashcards: Word Translations

We have three dogs: Joule, Newton, and Toby. Joule is three years older than twice Newton's age. Newton is Toby's age younger than eleven years. Toby is one year younger than Joules age. Find the age of each dog.

Joule: 9 years

Newton: 3 years

Toby: 8 year

Joule: 5 years

Newton: Not born yet

Toby: 1 year

Joule: 8 years

Newton: 4 years

Toby: 8 year

none of these

Joule: 12 years

Newton: 1 year

Toby: 5 year

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Flashcards: Word Translations

Joule: 9 years

Newton: 3 years

Toby: 8 year

Joule: 5 years

Newton: Not born yet

Toby: 1 year

Joule: 8 years

Newton: 4 years

Toby: 8 year

none of these

Joule: 12 years

Newton: 1 year

Toby: 5 year

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Flashcards: Word Translations

Your answer:

Joule: 5 years

Newton: Not born yet

Toby: 1 year

Your answer:

Joule: 8 years

Newton: 4 years

Toby: 8 year

Your answer:

none of these

Your answer:

Joule: 12 years

Newton: 1 year

Toby: 5 year

Correct answer:

Joule: 9 years

Newton: 3 years

Toby: 8 year

Explanation:

First, translate the problem into three equations. The statement, "Joule is three years older than twice Newton's age" is mathematically translated as

J=3+2N $\displaystyle J=3+2N$

where $\displaystyle J$ represents Joule's age and $\displaystyle N$ is Newton's age.

The statement, "Newton is Toby's age younger than eleven years" is translated as

N=11-T $\displaystyle N=11-T$

where $\displaystyle T$ is Toby's age.

The third statement, "Toby is one year younger than Joule" is

T=J-1 $\displaystyle T=J-1$.

So these are our three equations. To figure out the age of these dogs, first I will plug the third equation into the second equation. We get

$\displaystyle N=11-J+1$

N=12-J $\displaystyle N=12-J$

Plug this equation into the first equation to get

$\displaystyle J=3+2(12-J)$

$\displaystyle J=3+24-2J$

J=27-2J $\displaystyle J=27-2J$

Solve for $\displaystyle J$. Add $\displaystyle 2J$ to both sides

$\displaystyle J+2J=27-2J+2J$

3J=27 $\displaystyle 3J=27$

Divide both sides by 3

$\frac{3J}{3}=\frac{27}{3}$ $\displaystyle \frac{3J}{3}=\frac{27}{3}$

J=9 $\displaystyle J=9$

So Joules is 9 years old. Plug this value into the third equation to find Toby's age

T=J-1 $\displaystyle T=J-1$

T=9-1 $\displaystyle T=9-1$

T=8 $\displaystyle T=8$

Toby is 8 years old. Use this value to find Newton's age using the second equation

N=11-T $\displaystyle N=11-T$

N=11-8 $\displaystyle N=11-8$

N=3 $\displaystyle N=3$

Now, we have the age of the following dogs:

Joule: 9 years

Newton: 3 years

Toby: 8 years

Flashcards: Word Translations

Teachers at an elementary school have devised a system where a student's good behavior earns him or her tokens. Examples of such behavior include sitting quietly in a seat and completing an assignment on time. Jim sits quietly in his seat 2 times and completes assignments 3 times, earning himself 27 tokens. Jessica sits quietly in her seat 9 times and completes 6 assignments, earning herself 69 tokens. How many tokens is each of these two behaviors worth?

Sitting quietly is worth 9 tokens and completing an assignment is worth 3.

Sitting quietly is worth 3 tokens and completing an assignment is worth 9.

Sitting quietly is worth 7 tokens and completing an assignment is worth 3.

Sitting quietly is worth 3 tokens and completing an assignment is worth 7.

Sitting quietly and completing an assignment are each worth 4 tokens.

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Flashcards: Word Translations

Your answer:

Sitting quietly is worth 9 tokens and completing an assignment is worth 3.

Your answer:

Sitting quietly is worth 3 tokens and completing an assignment is worth 9.

Your answer:

Sitting quietly is worth 7 tokens and completing an assignment is worth 3.

Your answer:

Sitting quietly and completing an assignment are each worth 4 tokens.

Correct answer:

Sitting quietly is worth 3 tokens and completing an assignment is worth 7.

Explanation:

Since this is a long word problem, it might be easy to confuse the two behaviors and come up with the wrong answer. Let's avoid this problem by turning each behavior into a variable. If we call "sitting quietly" $\displaystyle x$ and "completing assignments" $\displaystyle y$, then we can easily construct a simple system of equations,

$\displaystyle 2x+3y=27$

and

$\displaystyle 9x+6y=69$.

We can multiply the first equation by $\displaystyle -2$ to yield $\displaystyle -4x-6y=-54$.

This allows us to cancel the $\displaystyle y$ terms when we add the two equations together. We get 5x=15 $\displaystyle 5x=15$, or x=3 $\displaystyle x=3$.

A quick substitution tells us that y=7 $\displaystyle y=7$. So, sitting quietly is worth 3 tokens and completing an assignment on time is worth 7.

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Flashcards: Word Translations

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