Math / Algebra

QuestionFlannery used 30 lilies and 78 roses to create six identical flower arrangements.
Write an equation to describe the relationship between $l$ , the number of lilies, and $r$ , the number of roses. Do NOT use a mixed number. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find a single equation that relates the number of lilies and roses in these identical flower arrangements. Watch out! Don't mix up the total number of flowers with the number in each arrangement!

STEP 2

1. Flowers per arrangement
2. Relate lilies and roses

STEP 3

We know Flannery made six identical arrangements.
That means each arrangement has the same number of lilies and the same number of roses!
She used a total of $30$ lilies.
So, to find the number of lilies per arrangement, we divide the total number of lilies by the number of arrangements: $30 \div 6 = 5$ .
Each arrangement has 5 lilies!

STEP 4

She used $78$ roses total, and made $6$ identical arrangements.
So each arrangement has $78 \div 6 = 13$ roses.
Each arrangement has 13 roses!

STEP 5

Let $l$ be the total number of lilies and $r$ be the total number of roses.
We know that there are $6$ arrangements, and each has $5$ lilies, so $l = 6 \cdot 5$ .
Similarly, each arrangement has $13$ roses, so $r = 6 \cdot 13$ .

STEP 6

We want to relate $l$ and $r$ directly, without the number of arrangements.
Notice that $l = 6 \cdot 5$ , so dividing both sides by 5 gives us $6 = \frac{l}{5}$ .
Also, $r = 6 \cdot 13$ , so dividing both sides by 13 gives us $6 = \frac{r}{13}$ .

STEP 7

Since both $\frac{l}{5}$ and $\frac{r}{13}$ are equal to $6$ , they must be equal to each other!
Therefore, our equation is $\frac{l}{5} = \frac{r}{13}$ .
Awesome!

STEP 8

The equation that describes the relationship between $l$ , the number of lilies, and $r$ , the number of roses is: $\frac{l}{5} = \frac{r}{13}$

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QuestionFlannery used 30 lilies and 78 roses to create six identical flower arrangements.
Write an equation to describe the relationship between $l$ , the number of lilies, and $r$ , the number of roses. Do NOT use a mixed number. $\square$

Studdy Solution

STEP 1

What is this asking? We need to find a single equation that relates the number of lilies and roses in these identical flower arrangements. Watch out! Don't mix up the total number of flowers with the number in each arrangement!

STEP 2

1. Flowers per arrangement
2. Relate lilies and roses

STEP 3

STEP 4

She used $78$ roses total, and made $6$ identical arrangements.
So each arrangement has $78 \div 6 = 13$ roses.
Each arrangement has 13 roses!

STEP 5

Let $l$ be the total number of lilies and $r$ be the total number of roses.
We know that there are $6$ arrangements, and each has $5$ lilies, so $l = 6 \cdot 5$ .
Similarly, each arrangement has $13$ roses, so $r = 6 \cdot 13$ .

STEP 6

We want to relate $l$ and $r$ directly, without the number of arrangements.
Notice that $l = 6 \cdot 5$ , so dividing both sides by 5 gives us $6 = \frac{l}{5}$ .
Also, $r = 6 \cdot 13$ , so dividing both sides by 13 gives us $6 = \frac{r}{13}$ .

STEP 7

Since both $\frac{l}{5}$ and $\frac{r}{13}$ are equal to $6$ , they must be equal to each other!
Therefore, our equation is $\frac{l}{5} = \frac{r}{13}$ .
Awesome!

STEP 8

The equation that describes the relationship between $l$ , the number of lilies, and $r$ , the number of roses is: $\frac{l}{5} = \frac{r}{13}$

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QuestionFlannery used 30 lilies and 78 roses to create six identical flower arrangements.Write an equation to describe the relationship between lll, the number of lilies, and rrr, the number of roses. Do NOT use a mixed number. □\square□

Studdy Solution

STEP 1

What is this asking? We need to find a single equation that relates the number of lilies and roses in these **identical** flower arrangements. Watch out! Don't mix up the total number of flowers with the number in each arrangement!

STEP 2

1. Flowers per arrangement2. Relate lilies and roses

STEP 3

STEP 4

She used 787878 roses total, and made 666 identical arrangements.So each arrangement has 78÷6=1378 \div 6 = 1378÷6=13 roses.Each arrangement has **13 roses**!

STEP 5

Let lll be the *total* number of lilies and rrr be the *total* number of roses.We know that there are 666 arrangements, and each has 555 lilies, so l=6⋅5l = 6 \cdot 5l=6⋅5.Similarly, each arrangement has 131313 roses, so r=6⋅13r = 6 \cdot 13r=6⋅13.

STEP 6

We want to relate lll and rrr *directly*, without the number of arrangements.Notice that l=6⋅5l = 6 \cdot 5l=6⋅5, so dividing both sides by 5 gives us 6=l56 = \frac{l}{5}6=5l​.Also, r=6⋅13r = 6 \cdot 13r=6⋅13, so dividing both sides by 13 gives us 6=r136 = \frac{r}{13}6=13r​.

STEP 7

Since both l5\frac{l}{5}5l​ and r13\frac{r}{13}13r​ are equal to 666, they must be equal to each other!Therefore, our equation is l5=r13\frac{l}{5} = \frac{r}{13}5l​=13r​.Awesome!

STEP 8

The equation that describes the relationship between lll, the number of lilies, and rrr, the number of roses is: l5=r13\frac{l}{5} = \frac{r}{13}5l​=13r​

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Start learning now

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

QuestionFlannery used 30 lilies and 78 roses to create six identical flower arrangements.
Write an equation to describe the relationship between $l$ , the number of lilies, and $r$ , the number of roses. Do NOT use a mixed number. $\square$

What is this asking? We need to find a single equation that relates the number of lilies and roses in these identical flower arrangements. Watch out! Don't mix up the total number of flowers with the number in each arrangement!

1. Flowers per arrangement
2. Relate lilies and roses

She used $78$ roses total, and made $6$ identical arrangements.
So each arrangement has $78 \div 6 = 13$ roses.
Each arrangement has 13 roses!

Let $l$ be the total number of lilies and $r$ be the total number of roses.
We know that there are $6$ arrangements, and each has $5$ lilies, so $l = 6 \cdot 5$ .
Similarly, each arrangement has $13$ roses, so $r = 6 \cdot 13$ .

We want to relate $l$ and $r$ directly, without the number of arrangements.
Notice that $l = 6 \cdot 5$ , so dividing both sides by 5 gives us $6 = \frac{l}{5}$ .
Also, $r = 6 \cdot 13$ , so dividing both sides by 13 gives us $6 = \frac{r}{13}$ .

Since both $\frac{l}{5}$ and $\frac{r}{13}$ are equal to $6$ , they must be equal to each other!
Therefore, our equation is $\frac{l}{5} = \frac{r}{13}$ .
Awesome!

The equation that describes the relationship between $l$ , the number of lilies, and $r$ , the number of roses is: $\frac{l}{5} = \frac{r}{13}$