Question

You are preparing for a party and need to know how many cans of soda to buy. You know that you want four cans, and you estimate that each of your friends will drink three cans. You set up an arithmetic equation to calculate the number of cans of soda for n friends, c=4+(n-1)⋅3. Match each term in the sequence with the correct number of cans.

Answer 1

Given the arithmetic equation below

`\begin{gathered} c=4+(n-1)\cdot3 \\ Where \\ n\text{ is the of friends \lparen term\rparen} \\ c\text{ is the number of cans of soda} \end{gathered}`

1) For term 6, i.e. n = 6,

Substitute 6 for n into the equation above

`\begin{gathered} c=4+\left(6-1\right)\cdot \:3 \\ c=4+(5)(3)=4+15=19 \\ c=19 \end{gathered}`

Hence, answer is b (19 cans)

2) For term 4, i.e. n = 4,

Substitute 4 for n into the equation above

`\begin{gathered} c=4+\left(4-1\right)\cdot \:3 \\ c=4+(3)(3=4+9=13 \\ c=13 \end{gathered}`

Hence, the answer is d (13 cans)

3) For term 2, i.e. n = 2,

Substitute 2 for n into the equation above

`\begin{gathered} c=4+\left(2-1\right)\cdot \:3 \\ c=4+(1)(3)=4+3=7 \\ c=7 \end{gathered}`

Hence, the answer is a (7 cans)

4) For term 1, i.e. n = 1

Substitute 1 for n into the equation above

`\begin{gathered} c=4+\left(1-1\right)\cdot \:3 \\ c=4+(0)(3)=4+0=4 \\ c=4 \end{gathered}`

Hence, the answer is c (4 cans)