Math / Algebra

QuestionApplication: 5 Marks
7. A catering company charges $\$ 590$ for 20 guests and $\$ 740$ for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]

Studdy Solution

STEP 1

What is this asking? If a catering company's price changes when the number of guests changes, how much does each extra guest cost? Watch out! Don't mix up the total cost with the cost per person!

STEP 2

1. Find the change in cost.
2. Find the change in guests.
3. Calculate the cost per additional guest.
4. Calculate the initial cost.
5. Calculate the cost per person.

STEP 3

Alright, let's kick things off!
We're given that the cost for 20 guests is $\$590$ and the cost for 26 guests is $\$740$ .
Let's find out how much more expensive it got with the extra guests.

STEP 4

Let $\Delta C$ be the change in cost.
We subtract the initial cost from the final cost: $\Delta C = \$740 - \$590 = \$150$ So, the cost increased by $\$\textbf{150}$ !

STEP 5

Now, let's see how many more guests caused that price jump.

STEP 6

Let $\Delta G$ be the change in the number of guests.
We subtract the initial number of guests from the final number of guests: $\Delta G = 26 - 20 = \textbf{6}$ Six extra guests!

STEP 7

Now, let's figure out how much each of those extra guests cost.

STEP 8

Let $c$ be the cost per additional guest.
We divide the change in cost by the change in the number of guests: $c = \frac{\Delta C}{\Delta G} = \frac{\$150}{6} = \$\textbf{25}$ Each additional guest costs $\$25$ !
Makes sense!

STEP 9

We know the total cost for 20 guests and the cost of each additional guest.
Let's work backward to find the initial cost, before those extra guests were added.

STEP 10

The cost increase due to the additional 6 guests is $6 \cdot \$25 = \$150$ .
The total cost for 26 guests was $\$740$ .
So, the initial cost, let's call it $I$ , plus the cost of the extra guests, equals the total cost for 26 guests: $I + \$150 = \$740$ $I = \$740 - \$150 = \$\textbf{590}$ This matches the given cost for 20 guests.
Perfect!

STEP 11

Alternatively, we could have used the cost for 20 guests directly as the initial cost, which is $\$590$ .

STEP 12

Now, let's put it all together!
We know the initial cost for 20 guests is $\$590$ .

STEP 13

Let $p$ be the cost per person.
We divide the initial cost by the initial number of guests: $p = \frac{\$590}{20} = \$\textbf{29.50}$ So, each person costs $\$29.50$ !

STEP 14

The cost per person is $\$29.50$ .

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QuestionApplication: 5 Marks
7. A catering company charges $\$ 590$ for 20 guests and $\$ 740$ for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]

Studdy Solution

STEP 1

What is this asking? If a catering company's price changes when the number of guests changes, how much does each extra guest cost? Watch out! Don't mix up the total cost with the cost per person!

STEP 2

1. Find the change in cost.
2. Find the change in guests.
3. Calculate the cost per additional guest.
4. Calculate the initial cost.
5. Calculate the cost per person.

STEP 3

Alright, let's kick things off!
We're given that the cost for 20 guests is $\$590$ and the cost for 26 guests is $\$740$ .
Let's find out how much more expensive it got with the extra guests.

STEP 4

Let $\Delta C$ be the change in cost.
We subtract the initial cost from the final cost: $\Delta C = \$740 - \$590 = \$150$ So, the cost increased by $\$\textbf{150}$ !

STEP 5

Now, let's see how many more guests caused that price jump.

STEP 6

Let $\Delta G$ be the change in the number of guests.
We subtract the initial number of guests from the final number of guests: $\Delta G = 26 - 20 = \textbf{6}$ Six extra guests!

STEP 7

Now, let's figure out how much each of those extra guests cost.

STEP 8

Let $c$ be the cost per additional guest.
We divide the change in cost by the change in the number of guests: $c = \frac{\Delta C}{\Delta G} = \frac{\$150}{6} = \$\textbf{25}$ Each additional guest costs $\$25$ !
Makes sense!

STEP 9

We know the total cost for 20 guests and the cost of each additional guest.
Let's work backward to find the initial cost, before those extra guests were added.

STEP 10

STEP 11

Alternatively, we could have used the cost for 20 guests directly as the initial cost, which is $\$590$ .

STEP 12

Now, let's put it all together!
We know the initial cost for 20 guests is $\$590$ .

STEP 13

Let $p$ be the cost per person.
We divide the initial cost by the initial number of guests: $p = \frac{\$590}{20} = \$\textbf{29.50}$ So, each person costs $\$29.50$ !

STEP 14

The cost per person is $\$29.50$ .

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QuestionApplication: 5 Marks7. A catering company charges $590\$ 590$590 for 20 guests and $740\$ 740$740 for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]

Studdy Solution

STEP 1

What is this asking? If a catering company's price changes when the number of guests changes, how much does each extra guest cost? Watch out! Don't mix up the total cost with the cost *per person*!

STEP 2

1. Find the change in cost.2. Find the change in guests.3. Calculate the cost per additional guest.4. Calculate the initial cost.5. Calculate the cost per person.

STEP 3

Alright, let's **kick things off**!We're given that the cost for 20 guests is $590\$590$590 and the cost for 26 guests is $740\$740$740.Let's find out how much *more* expensive it got with the extra guests.

STEP 4

Let ΔC\Delta CΔC be the change in cost.We **subtract** the initial cost from the final cost: ΔC=$740−$590=$150 \Delta C = \$740 - \$590 = \$150 ΔC=$740−$590=$150 So, the cost increased by $150\$\textbf{150}$150!

STEP 5

Now, let's see how many *more* guests caused that price jump.

STEP 6

Let ΔG\Delta GΔG be the change in the number of guests.We **subtract** the initial number of guests from the final number of guests: ΔG=26−20=6 \Delta G = 26 - 20 = \textbf{6} ΔG=26−20=6 Six extra guests!

STEP 7

Now, let's figure out how much *each* of those extra guests cost.

STEP 8

Let ccc be the cost per additional guest.We **divide** the change in cost by the change in the number of guests: c=ΔCΔG=$1506=$25 c = \frac{\Delta C}{\Delta G} = \frac{\$150}{6} = \$\textbf{25} c=ΔGΔC​=6$150​=$25 Each additional guest costs $25\$25$25!Makes sense!

STEP 9

We know the total cost for 20 guests and the cost of *each* additional guest.Let's **work backward** to find the initial cost, *before* those extra guests were added.

STEP 10

STEP 11

Alternatively, we could have used the cost for 20 guests directly as the initial cost, which is $590\$590$590.

STEP 12

Now, let's **put it all together**!We know the initial cost for 20 guests is $590\$590$590.

STEP 13

Let ppp be the cost per person.We **divide** the initial cost by the initial number of guests: p=$59020=$29.50 p = \frac{\$590}{20} = \$\textbf{29.50} p=20$590​=$29.50 So, each person costs $29.50\$29.50$29.50!

STEP 14

The cost per person is $29.50\$29.50$29.50.

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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.

QuestionApplication: 5 Marks
7. A catering company charges $\$ 590$ for 20 guests and $\$ 740$ for 26 guests. What is the cost per person? Provide "let" statements and show all calculations. [2 Marks]

What is this asking? If a catering company's price changes when the number of guests changes, how much does each extra guest cost? Watch out! Don't mix up the total cost with the cost per person!

1. Find the change in cost.
2. Find the change in guests.
3. Calculate the cost per additional guest.
4. Calculate the initial cost.
5. Calculate the cost per person.

Alright, let's kick things off!
We're given that the cost for 20 guests is $\$590$ and the cost for 26 guests is $\$740$ .
Let's find out how much more expensive it got with the extra guests.

Let $\Delta C$ be the change in cost.
We subtract the initial cost from the final cost: $\Delta C = \$740 - \$590 = \$150$ So, the cost increased by $\$\textbf{150}$ !

Now, let's see how many more guests caused that price jump.

Let $\Delta G$ be the change in the number of guests.
We subtract the initial number of guests from the final number of guests: $\Delta G = 26 - 20 = \textbf{6}$ Six extra guests!

Now, let's figure out how much each of those extra guests cost.

Let $c$ be the cost per additional guest.
We divide the change in cost by the change in the number of guests: $c = \frac{\Delta C}{\Delta G} = \frac{\$150}{6} = \$\textbf{25}$ Each additional guest costs $\$25$ !
Makes sense!

We know the total cost for 20 guests and the cost of each additional guest.
Let's work backward to find the initial cost, before those extra guests were added.

Alternatively, we could have used the cost for 20 guests directly as the initial cost, which is $\$590$ .

Now, let's put it all together!
We know the initial cost for 20 guests is $\$590$ .

Let $p$ be the cost per person.
We divide the initial cost by the initial number of guests: $p = \frac{\$590}{20} = \$\textbf{29.50}$ So, each person costs $\$29.50$ !

The cost per person is $\$29.50$ .