Question

1. for each of the following, turn the information into an equation and solve the equation.

(a) the sum of a number ( n ) and 11 is equal to 25. find the number ( n ).
(b) eight less than a number ( x ) is equal to 12. find the number ( x ).
(c) six times a number ( y ) is equal to 72. find the number ( y )
(d) when the number ( c ) is divided by six, the result is 48. find the number ( c ).
(e) one - fourth of a number ( k ) is equal to 15. find the number ( k ).
(f) when you double the number ( n ), the result is equal to 34. find the number ( n ).

1. for each of the following, turn the information into an equation and solve the equation. simplify your answers and convert any improper fractions into mixed numbers.

(a) two - fifths of a number ( n ) is equal to six. find the number ( n )
(b) four - sevenths of a number ( x ) is equal to sixteen - thirds. find the number ( x ).

Explanation:

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Problem 1(a)

Step1: Translate to equation

$n + 11 = 25$

Step2: Isolate $n$ (subtract 11)

$n = 25 - 11$
$n = 14$

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Problem 1(b)

Step1: Translate to equation

$x - 8 = 12$

Step2: Isolate $x$ (add 8)

$x = 12 + 8$
$x = 20$

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Problem 1(c)

Step1: Translate to equation

$6y = 72$

Step2: Isolate $y$ (divide by 6)

$y = \frac{72}{6}$
$y = 12$

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Problem 1(d)

Step1: Translate to equation

$\frac{c}{6} = 48$

Step2: Isolate $c$ (multiply by 6)

$c = 48 \times 6$
$c = 288$

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Problem 1(e)

Step1: Translate to equation

$\frac{1}{4}k = 15$

Step2: Isolate $k$ (multiply by 4)

$k = 15 \times 4$
$k = 60$

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Problem 1(f)

Step1: Translate to equation

$2n = 34$

Step2: Isolate $n$ (divide by 2)

$n = \frac{34}{2}$
$n = 17$

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Problem 2(a)

Step1: Translate to equation

$\frac{2}{5}n = 6$

Step2: Isolate $n$ (multiply by $\frac{5}{2}$)

$n = 6 \times \frac{5}{2}$
$n = 15$

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Problem 2(b)

Step1: Translate to equation

$\frac{4}{7}x = \frac{16}{3}$

Step2: Isolate $x$ (multiply by $\frac{7}{4}$)

$x = \frac{16}{3} \times \frac{7}{4}$
$x = \frac{112}{12} = \frac{28}{3}$

Step3: Convert to mixed number

$x = 9\frac{1}{3}$

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Answer:

1. (a) $n=14$
2. (b) $x=20$
3. (c) $y=12$
4. (d) $c=288$
5. (e) $k=60$
6. (f) $n=17$
7. (a) $n=15$
8. (b) $x=9\frac{1}{3}$