Question

writing equations
write the following equations:

1. sixteen is four more than x.
2. twenty-four is half of x.
3. x decreased by five is twenty-one.
4. one more than twice x is seventeen.
5. ninety-four is thirteen less than x.
6. the quotient of x and two is seven.
7. the product of five and x is thirty-five.
8. the sum of x and forty-three is eighty-four.
9. the difference of x and eighteen is thirty-six.
10. one number is eight times another number.
11. one number is five less than another number.
12. the sum of three consecutive whole numbers is eighteen.
13. one number is four more than another number.
14. eight more than twice a number is 24.
15. double a number, increased by nine, is twenty-five.
16. triple a number, decreased by six, is twenty-one.
17. text obscured
18. text obscured
19. double a number plus twenty-four is eight times the number.
20. thirty divided by a number is four times the number.

Explanation:

Step1: Translate verbal to equation

$16 = x + 4$

Step2: Translate verbal to equation

$24 = \frac{1}{2}x$

Step3: Translate verbal to equation

$\frac{x}{5} = 21$

Step4: Translate verbal to equation

$2x + 1 = 17$

Step5: Translate verbal to equation

$94 = x - 13$

Step6: Translate verbal to equation

$\frac{x}{2} = 7$

Step7: Translate verbal to equation

$5x = 35$

Step8: Translate verbal to equation

$x + 43 = 84$

Step9: Translate verbal to equation

$x - 18 = 36$

Step10: Translate verbal to equation

Let first number = $a$, second = $b$; $a = 8b$

Step11: Translate verbal to equation

Let first number = $a$, second = $b$; $a = b - 5$

Step12: Translate verbal to equation

Let first number = $n$; $n + (n+1) + (n+2) = 18$

Step13: Translate verbal to equation

Let first number = $a$, second = $b$; $a = b + 4$

Step14: Translate verbal to equation

Let number = $x$; $2x + 8 = 24$

Step15: Translate verbal to equation

Let number = $x$; $2x + 9 = 25$

Step16: Translate verbal to equation

Let number = $x$; $3x - 6 = 21$

Step19: Translate verbal to equation

Let number = $x$; $2x + 24 = 8x$

Step20: Translate verbal to equation

Let number = $x$; $36 - x = 4x$

Answer:

1. $16 = x + 4$
2. $24 = \frac{1}{2}x$
3. $\frac{x}{5} = 21$
4. $2x + 1 = 17$
5. $94 = x - 13$
6. $\frac{x}{2} = 7$
7. $5x = 35$
8. $x + 43 = 84$
9. $x - 18 = 36$
10. $a = 8b$ (where $a,b$ are the two numbers)
11. $a = b - 5$ (where $a,b$ are the two numbers)
12. $n + (n+1) + (n+2) = 18$ (where $n$ is the first consecutive number)
13. $a = b + 4$ (where $a,b$ are the two numbers)
14. $2x + 8 = 24$ (where $x$ is the number)
15. $2x + 9 = 25$ (where $x$ is the number)
16. $3x - 6 = 21$ (where $x$ is the number)
17. $2x + 24 = 8x$ (where $x$ is the number)
18. $36 - x = 4x$ (where $x$ is the number)

(Note: Problems 17 and 18 are illegible in the image and cannot be translated accurately.)