Question

3. Tyler needs to complete this table for his consumer science class. He knowsthat 1 tablespoon contains 3 teaspoons and that 1 cup contains 16 tablespoons.3a. Complete the missing values in the table.missing value)number of teaspoonsnumber of tablespoonsnumber of cups96A?23612B?

Answer 1

Write out the given information

`\begin{gathered} 1\text{ tablespoon=3 teaspoons } \\ \text{And } \\ 1\text{ cup=16 tablespoons} \end{gathered}`

For The first missing value, A=?

`\begin{gathered} \text{Number of teaspoon=96} \\ \text{Number of tablespoon=A} \\ \text{Number of cups=2} \end{gathered}`

From the information given

`\begin{gathered} 1\text{ tablespoon=3 teaspoon} \\ \text{Then } \\ A\text{ tablespoon=96 teaspoon} \end{gathered}`

Hence

`\begin{gathered} A=(96)/(3)=32 \\ \text{Hence } \\ 32\text{ tablespoon=96 teaspoon } \end{gathered}`

Therefore

A=32

For the second missing value, B=?

`\begin{gathered} \text{ Recall that } \\ 1\text{ cup=16tablespoon } \\ B\text{ cups=12 tablespoon } \end{gathered}`

Hence

`B=(12)/(16)=(3)/(4)\text{cup}`

Therefore

B=3/4

For third missing value C=?

`\begin{gathered} \text{ Recall that } \\ 1\text{ tablespoon = 3 teaspoons} \\ 48\text{ tablespoon=C teaspoons } \end{gathered}`

Then

`\begin{gathered} C=3*48=144 \\ \text{Hence } \\ 48\text{ tablespoon = 144 teaspoon } \end{gathered}`

Therefore

C=144

The equation that represent the number of teaspoon t contained in a cup C

`\begin{gathered} \text{The number of teaspoon = t} \\ \text{the number of cup=c} \\ Since\text{ 1 tablespoon =3teaspoon } \\ And\text{ 1 cup = 16 tablespoon } \\ \text{hence } \\ 1\text{ cup=48 teaspoon } \end{gathered}`

Hence

`\begin{gathered} t=48C \\ \text{Where } \\ t=Number\text{ of teaspoon } \\ C=\text{ Number of cup } \end{gathered}`

The equation is

t = 48 C