Math / Algebra

QuestionSolve the proportion.
16. $\frac{5}{6}=\frac{15}{4 x}$
17. $\frac{8}{12}=\frac{71.5}{x}$
18. $\frac{6}{13}=\frac{t+4}{18}$

Studdy Solution

STEP 1

What is this asking? We need to find the mystery values of $x$ and $t$ that make these fractions equal! Watch out! Don't forget to keep your calculations neat and organized.
A little slip-up with the numbers can lead you astray!

STEP 2

1. Solve for $x$ in the first proportion.
2. Solve for $x$ in the second proportion.
3. Solve for $t$ in the third proportion.

STEP 3

We cross-multiply to get rid of those pesky fractions!
This works because we're really multiplying both sides by the denominators.
So we have $5 \cdot 4x = 15 \cdot 6$ .

STEP 4

This simplifies to $20x = 90$ .
See how much cleaner that looks?

STEP 5

Now, we want that $x$ all alone, so we divide both sides by $\textbf{20}$ .
Remember, what we do to one side, we must do to the other.
This gives us $x = \frac{90}{20}$ .

STEP 6

We can simplify the fraction by dividing the top and bottom by their greatest common divisor, which is $\textbf{10}$ .
This gives us $x = \frac{9}{2}$ , or $x = \textbf{4.5}$ !

STEP 7

Just like before, we cross-multiply to get $8 \cdot x = 71.5 \cdot 12$ .

STEP 8

This becomes $8x = 858$ .
Looking good!

STEP 9

We want $x$ by itself, so we divide both sides by $\textbf{8}$ .
This gives us $x = \frac{858}{8}$ .

STEP 10

Now we simplify the fraction to get $x = \textbf{107.25}$ !
Boom!

STEP 11

You know the drill! Cross-multiply to get $6 \cdot 18 = 13 \cdot (t+4)$ .

STEP 12

This simplifies to $108 = 13(t+4)$ .

STEP 13

Now we distribute that $\textbf{13}$ to both terms inside the parentheses.
This gives us $108 = 13t + 52$ .

STEP 14

We're getting closer!
We want to get that $13t$ term by itself, so we subtract $\textbf{52}$ from both sides.
This gives us $108 - 52 = 13t$ , which simplifies to $56 = 13t$ .

STEP 15

Almost there! Divide both sides by $\textbf{13}$ to get $t = \frac{56}{13}$ .

STEP 16

This fraction can't be simplified any further, so our final answer is $t = \frac{\textbf{56}}{\textbf{13}}$ !

STEP 17

We found $x = 4.5$ for the first proportion, $x = 107.25$ for the second, and $t = \frac{56}{13}$ for the third!

Was this helpful?

QuestionSolve the proportion.
16. $\frac{5}{6}=\frac{15}{4 x}$
17. $\frac{8}{12}=\frac{71.5}{x}$
18. $\frac{6}{13}=\frac{t+4}{18}$

Studdy Solution

STEP 1

What is this asking? We need to find the mystery values of $x$ and $t$ that make these fractions equal! Watch out! Don't forget to keep your calculations neat and organized.
A little slip-up with the numbers can lead you astray!

STEP 2

1. Solve for $x$ in the first proportion.
2. Solve for $x$ in the second proportion.
3. Solve for $t$ in the third proportion.

STEP 3

We cross-multiply to get rid of those pesky fractions!
This works because we're really multiplying both sides by the denominators.
So we have $5 \cdot 4x = 15 \cdot 6$ .

STEP 4

This simplifies to $20x = 90$ .
See how much cleaner that looks?

STEP 5

Now, we want that $x$ all alone, so we divide both sides by $\textbf{20}$ .
Remember, what we do to one side, we must do to the other.
This gives us $x = \frac{90}{20}$ .

STEP 6

We can simplify the fraction by dividing the top and bottom by their greatest common divisor, which is $\textbf{10}$ .
This gives us $x = \frac{9}{2}$ , or $x = \textbf{4.5}$ !

STEP 7

Just like before, we cross-multiply to get $8 \cdot x = 71.5 \cdot 12$ .

STEP 8

This becomes $8x = 858$ .
Looking good!

STEP 9

We want $x$ by itself, so we divide both sides by $\textbf{8}$ .
This gives us $x = \frac{858}{8}$ .

STEP 10

Now we simplify the fraction to get $x = \textbf{107.25}$ !
Boom!

STEP 11

You know the drill! Cross-multiply to get $6 \cdot 18 = 13 \cdot (t+4)$ .

STEP 12

This simplifies to $108 = 13(t+4)$ .

STEP 13

Now we distribute that $\textbf{13}$ to both terms inside the parentheses.
This gives us $108 = 13t + 52$ .

STEP 14

We're getting closer!
We want to get that $13t$ term by itself, so we subtract $\textbf{52}$ from both sides.
This gives us $108 - 52 = 13t$ , which simplifies to $56 = 13t$ .

STEP 15

Almost there! Divide both sides by $\textbf{13}$ to get $t = \frac{56}{13}$ .

STEP 16

This fraction can't be simplified any further, so our final answer is $t = \frac{\textbf{56}}{\textbf{13}}$ !

STEP 17

We found $x = 4.5$ for the first proportion, $x = 107.25$ for the second, and $t = \frac{56}{13}$ for the third!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the proportion.16. 56=154x\frac{5}{6}=\frac{15}{4 x}65​=4x15​17. 812=71.5x\frac{8}{12}=\frac{71.5}{x}128​=x71.5​18. 613=t+418\frac{6}{13}=\frac{t+4}{18}136​=18t+4​

Studdy Solution

STEP 1

What is this asking? We need to find the mystery values of xxx and ttt that make these fractions equal! Watch out! Don't forget to keep your calculations neat and organized.A little slip-up with the numbers can lead you astray!

STEP 2

1. Solve for xxx in the first proportion.2. Solve for xxx in the second proportion.3. Solve for ttt in the third proportion.

STEP 3

We **cross-multiply** to get rid of those pesky fractions!This works because we're really multiplying both sides by the denominators.So we have 5⋅4x=15⋅65 \cdot 4x = 15 \cdot 65⋅4x=15⋅6.

STEP 4

This simplifies to 20x=9020x = 9020x=90.See how much cleaner that looks?

STEP 5

Now, we want that xxx all alone, so we **divide both sides** by 20\textbf{20}20.Remember, what we do to one side, we *must* do to the other.This gives us x=9020x = \frac{90}{20}x=2090​.

STEP 6

We can **simplify the fraction** by dividing the top and bottom by their greatest common divisor, which is 10\textbf{10}10.This gives us x=92x = \frac{9}{2}x=29​, or x=4.5x = \textbf{4.5}x=4.5!

STEP 7

Just like before, we **cross-multiply** to get 8⋅x=71.5⋅128 \cdot x = 71.5 \cdot 128⋅x=71.5⋅12.

STEP 8

This becomes 8x=8588x = 8588x=858.Looking good!

STEP 9

We want xxx by itself, so we **divide both sides** by 8\textbf{8}8.This gives us x=8588x = \frac{858}{8}x=8858​.

STEP 10

Now we **simplify the fraction** to get x=107.25x = \textbf{107.25}x=107.25!Boom!

STEP 11

You know the drill! **Cross-multiply** to get 6⋅18=13⋅(t+4)6 \cdot 18 = 13 \cdot (t+4)6⋅18=13⋅(t+4).

STEP 12

This simplifies to 108=13(t+4)108 = 13(t+4)108=13(t+4).

STEP 13

Now we **distribute** that 13\textbf{13}13 to both terms inside the parentheses.This gives us 108=13t+52108 = 13t + 52108=13t+52.

STEP 14

We're getting closer!We want to get that 13t13t13t term by itself, so we **subtract 52\textbf{52}52** from both sides.This gives us 108−52=13t108 - 52 = 13t108−52=13t, which simplifies to 56=13t56 = 13t56=13t.

STEP 15

Almost there! **Divide both sides** by 13\textbf{13}13 to get t=5613t = \frac{56}{13}t=1356​.

STEP 16

This fraction can't be simplified any further, so our **final answer** is t=5613t = \frac{\textbf{56}}{\textbf{13}}t=1356​!

STEP 17

We found x=4.5x = 4.5x=4.5 for the first proportion, x=107.25x = 107.25x=107.25 for the second, and t=5613t = \frac{56}{13}t=1356​ for the third!

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the proportion.
16. $\frac{5}{6}=\frac{15}{4 x}$
17. $\frac{8}{12}=\frac{71.5}{x}$
18. $\frac{6}{13}=\frac{t+4}{18}$

What is this asking? We need to find the mystery values of $x$ and $t$ that make these fractions equal! Watch out! Don't forget to keep your calculations neat and organized.
A little slip-up with the numbers can lead you astray!

1. Solve for $x$ in the first proportion.
2. Solve for $x$ in the second proportion.
3. Solve for $t$ in the third proportion.

We cross-multiply to get rid of those pesky fractions!
This works because we're really multiplying both sides by the denominators.
So we have $5 \cdot 4x = 15 \cdot 6$ .

This simplifies to $20x = 90$ .
See how much cleaner that looks?

Now, we want that $x$ all alone, so we divide both sides by $\textbf{20}$ .
Remember, what we do to one side, we must do to the other.
This gives us $x = \frac{90}{20}$ .

We can simplify the fraction by dividing the top and bottom by their greatest common divisor, which is $\textbf{10}$ .
This gives us $x = \frac{9}{2}$ , or $x = \textbf{4.5}$ !

Just like before, we cross-multiply to get $8 \cdot x = 71.5 \cdot 12$ .

This becomes $8x = 858$ .
Looking good!

We want $x$ by itself, so we divide both sides by $\textbf{8}$ .
This gives us $x = \frac{858}{8}$ .

Now we simplify the fraction to get $x = \textbf{107.25}$ !
Boom!

You know the drill! Cross-multiply to get $6 \cdot 18 = 13 \cdot (t+4)$ .

This simplifies to $108 = 13(t+4)$ .

Now we distribute that $\textbf{13}$ to both terms inside the parentheses.
This gives us $108 = 13t + 52$ .

We're getting closer!
We want to get that $13t$ term by itself, so we subtract $\textbf{52}$ from both sides.
This gives us $108 - 52 = 13t$ , which simplifies to $56 = 13t$ .

Almost there! Divide both sides by $\textbf{13}$ to get $t = \frac{56}{13}$ .

This fraction can't be simplified any further, so our final answer is $t = \frac{\textbf{56}}{\textbf{13}}$ !

We found $x = 4.5$ for the first proportion, $x = 107.25$ for the second, and $t = \frac{56}{13}$ for the third!