Question

1. y raised to the fourth power.
2. one - fourth of a number.
3. x divided by three.

write the algebraic expression.

1. mary weighed x pounds. express algebraically her weight after she gained ten pounds.
2. samantha is y years old now. represent algebraically her age five years ago.
3. if john has x dollars and his sister ann has one - half as many, express algebraically the number of dollars ann has.
4. steve is y years old now. represent his age two years from now.
5. heather is x years old. marion is three times as old as heather. represent marion’s age.
6. if three pencils cost x cents, represent in cents the cost of one pencil.
7. the width of a rectangle is x inches. represent the length in inches if the length is eight times the width.

Explanation:

Step1: Translate "y raised to the fourth power"

$y^4$

Step2: Translate "One - fourth of a number"

Let the number be $n$, then it is $\frac{1}{4}n$. If we use the variable given in the general context of the problem set, assume the number is $x$, so it is $\frac{1}{4}x$

Step3: Translate "x divided by three"

$\frac{x}{3}$

Step4: Translate "Mary weighed x pounds. Her weight after she gained ten pounds"

$x + 10$

Step5: Translate "Samantha is y years old now. Her age five years ago"

$y-5$

Step6: Translate "John has x dollars and his sister Ann has one - half as many"

$\frac{1}{2}x$

Step7: Translate "Steve is y years old now. His age two years from now"

$y + 2$

Step8: Translate "Heather is x years old. Marion is three times as old as Heather"

$3x$

Step9: Translate "Three pencils cost x cents. Cost of one pencil"

$\frac{x}{3}$

Step10: Translate "Width of a rectangle is x inches. Length is eight times the width"

$8x$

Answer:

1. $y^4$
2. $\frac{1}{4}x$
3. $\frac{x}{3}$
4. $x + 10$
5. $y-5$
6. $\frac{1}{2}x$
7. $y + 2$
8. $3x$
9. $\frac{x}{3}$
10. $8x$