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Flashcards: Translating Words to Linear Equations

Jason is 10 years older than Alexa. Using $\displaystyle j$ to represent Jason's age and $\displaystyle a$ to represent Alexa's age, which of the following demonstrates the correct relationship between Jason's and Alexa's ages?

j=a-10 $\displaystyle j=a-10$

j=10+a $\displaystyle j=10+a$

j+a=10 $\displaystyle j+a=10$

j+10=a $\displaystyle j+10=a$

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Flashcards: Translating Words to Linear Equations

j=a-10 $\displaystyle j=a-10$

j=10+a $\displaystyle j=10+a$

j+a=10 $\displaystyle j+a=10$

j+10=a $\displaystyle j+10=a$

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Flashcards: Translating Words to Linear Equations

Your answer:

j=a-10 $\displaystyle j=a-10$

Your answer:

j+a=10 $\displaystyle j+a=10$

Your answer:

j+10=a $\displaystyle j+10=a$

Correct answer:

j=10+a $\displaystyle j=10+a$

Explanation:

Many words translate directly to mathematical symbols, and "is" is a great example: "is" means "equals" (if you were to say x is 6, then you could express that as x = 6, for example).

That helps here, because when you're told that "Jason is 10 years older than Alexa" you can put an equals sign right were "is" appears: j = $\displaystyle j =$ 10 years older than Alexa. Then to account for the rest of the equation, recognize that we need more than Alexa's current age to equal Jason's, so we'll use a + sign there, arriving at:

j=10+a $\displaystyle j=10+a$

Note that if you see a question like this on the SAT, it's helpful to choose numbers that work with the situation to check your answer. If Jason is 10 years older than Alexa, he might be 15 while she is 5. If you plug those in to the correct answer, you will see that it works:

15 = 10 + 5

Flashcards: Translating Words to Linear Equations

Riley and four friends went to dinner and agreed to split the bill evenly. If the bill came to $\displaystyle b$ dollars and the group left a 20% tip, which of the following represents the amount that each person paid?

$\frac{1.2b}{5}$ $\displaystyle \frac{1.2b}{5}$

$\frac{1.2b}{4}$ $\displaystyle \frac{1.2b}{4}$

1.2b $\displaystyle 1.2b$

$\frac{4b}{1.2}$ $\displaystyle \frac{4b}{1.2}$

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Flashcards: Translating Words to Linear Equations

Your answer:

$\frac{1.2b}{4}$ $\displaystyle \frac{1.2b}{4}$

Your answer:

1.2b $\displaystyle 1.2b$

Your answer:

$\frac{4b}{1.2}$ $\displaystyle \frac{4b}{1.2}$

Correct answer:

$\frac{1.2b}{5}$ $\displaystyle \frac{1.2b}{5}$

Explanation:

One important thing to identify in this problem is that Riley and her four friends went to dinner, meaning that there were 5 total people at dinner, not 4. Then you can see that the price of the dinner, $\displaystyle b$, plus 20% as a tip, would come out to 1.2b $\displaystyle 1.2b$. Because each person only pays their equal share, we divide that total amount of money, 1.2b $\displaystyle 1.2b$ by 5 to get our answer for what each of the five people had to pay:

$\frac{1.2b}{5}$ $\displaystyle \frac{1.2b}{5}$

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