Math / Algebra

QuestionIf $5 \mathrm{ab}=3.5$ and $\mathrm{ab} \mathrm{n}=17.5$ what is the value of $1 \mathrm{n}$ $\square$ Answer Preview:

Studdy Solution

STEP 1

1. We are given two equations: $5ab = 3.5$ and $ab \cdot n = 17.5$ .
2. We need to find the value of $n$ .
3. We assume $ab$ is a common term in both equations.

STEP 2

1. Solve the first equation for $ab$ .
2. Substitute the value of $ab$ into the second equation.
3. Solve for $n$ .

STEP 3

Start with the first equation:
$5ab = 3.5$
To isolate $ab$ , divide both sides by 5:
$ab = \frac{3.5}{5}$

STEP 4

Calculate the division:
$ab = 0.7$

STEP 5

Substitute $ab = 0.7$ into the second equation:
$0.7 \cdot n = 17.5$

STEP 6

To solve for $n$ , divide both sides by 0.7:
$n = \frac{17.5}{0.7}$

STEP 7

Calculate the division:
$n = 25$

STEP 8

The value of $n$ is:
$\boxed{25}$

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QuestionIf $5 \mathrm{ab}=3.5$ and $\mathrm{ab} \mathrm{n}=17.5$ what is the value of $1 \mathrm{n}$ $\square$ Answer Preview:

Studdy Solution

STEP 1

1. We are given two equations: $5ab = 3.5$ and $ab \cdot n = 17.5$ .
2. We need to find the value of $n$ .
3. We assume $ab$ is a common term in both equations.

STEP 2

1. Solve the first equation for $ab$ .
2. Substitute the value of $ab$ into the second equation.
3. Solve for $n$ .

STEP 3

Start with the first equation:
$5ab = 3.5$
To isolate $ab$ , divide both sides by 5:
$ab = \frac{3.5}{5}$

STEP 4

Calculate the division:
$ab = 0.7$

STEP 5

Substitute $ab = 0.7$ into the second equation:
$0.7 \cdot n = 17.5$

STEP 6

To solve for $n$ , divide both sides by 0.7:
$n = \frac{17.5}{0.7}$

STEP 7

Calculate the division:
$n = 25$

STEP 8

The value of $n$ is:
$\boxed{25}$

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QuestionIf 5ab=3.55 \mathrm{ab}=3.55ab=3.5 and abn=17.5\mathrm{ab} \mathrm{n}=17.5abn=17.5 what is the value of 1n1 \mathrm{n}1n □\square□ Answer Preview:

Studdy Solution

STEP 1

1. We are given two equations: 5ab=3.5 5ab = 3.5 5ab=3.5 and ab⋅n=17.5 ab \cdot n = 17.5 ab⋅n=17.5.2. We need to find the value of n n n.3. We assume ab ab ab is a common term in both equations.

STEP 2

1. Solve the first equation for ab ab ab.2. Substitute the value of ab ab ab into the second equation.3. Solve for n n n.

STEP 3

Start with the first equation:5ab=3.5 5ab = 3.5 5ab=3.5To isolate ab ab ab, divide both sides by 5:ab=3.55 ab = \frac{3.5}{5} ab=53.5​

STEP 4

Calculate the division:ab=0.7 ab = 0.7 ab=0.7

STEP 5

Substitute ab=0.7 ab = 0.7 ab=0.7 into the second equation:0.7⋅n=17.5 0.7 \cdot n = 17.5 0.7⋅n=17.5

STEP 6

To solve for n n n, divide both sides by 0.7:n=17.50.7 n = \frac{17.5}{0.7} n=0.717.5​

STEP 7

Calculate the division:n=25 n = 25 n=25

STEP 8

The value of n n n is:25 \boxed{25} 25​

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QuestionIf $5 \mathrm{ab}=3.5$ and $\mathrm{ab} \mathrm{n}=17.5$ what is the value of $1 \mathrm{n}$ $\square$ Answer Preview:

1. We are given two equations: $5ab = 3.5$ and $ab \cdot n = 17.5$ .
2. We need to find the value of $n$ .
3. We assume $ab$ is a common term in both equations.

1. Solve the first equation for $ab$ .
2. Substitute the value of $ab$ into the second equation.
3. Solve for $n$ .

Start with the first equation:
$5ab = 3.5$
To isolate $ab$ , divide both sides by 5:
$ab = \frac{3.5}{5}$

Calculate the division:
$ab = 0.7$

Substitute $ab = 0.7$ into the second equation:
$0.7 \cdot n = 17.5$

To solve for $n$ , divide both sides by 0.7:
$n = \frac{17.5}{0.7}$

Calculate the division:
$n = 25$

The value of $n$ is:
$\boxed{25}$