Question

ME A Pound of Tea POW ID: 4087 Problem Print Jonathan and Hazel love to drink tea. When they are both at home a pound of lea lasis two weeks Occasionally Hazel visits her mother in Australia. It takes six weeks for Jonathan alone to use up a pound orlea How long should a pound of tea lasi Hazel if she were alone? Extra Extra in 2006 Hazel visited her mother for six weeks in the spring in the summer Jonathan gave up drinking tea for six weeks Their favonte tea costs $9.00 per pound About how much did the couple spend on tea during the year?

Answer 1

A pound of tea would last for 6 divided by 3, which is 2 weeks for Hazel if she were alone.

Step-by-step explanation:

To find out how long a pound of tea would last for Hazel, we can use the information given. When both Jonathan and Hazel are at home, a pound of tea lasts for 2 weeks. When Jonathan is alone, it lasts for 6 weeks. Let's assume Hazel is alone at home. If a pound of tea lasts for 2 weeks when both Jonathan and Hazel are at home, and it lasts for 6 weeks when Jonathan is alone, we can conclude that Hazel drinks three times as much tea as Jonathan. Therefore, a pound of tea would last for 6 divided by 3, which is 2 weeks for Hazel if she were alone.

Answer 2

• 3 weeks

,

• $207

Step-by-step explanation:

Part A

• Let the time it takes Hazel to finish 1 pound of tea = x weeks

,

• Jonathan alone uses up a pound of tea in six weeks.

,

• When they are both at home a pound of tea lasts two weeks.

This gives rise to the equation below:

`(1)/(x)+(1)/(6)=(1)/(2)`

First, we solve for x:

`\begin{gathered} (1)/(x)=(1)/(2)-(1)/(6) \\ (1)/(x)=(3-1)/(6) \\ (1)/(x)=(2)/(6) \\ 2x=6 \\ x=3\text{ weeks} \end{gathered}`

If Hazel were alone, a pound of tea would last 3 weeks.

Part B

There are a total of 52 weeks in a year.

• Hazel did not drink tea for 6 weeks

,

• Jonathan gave up drinking tea for six weeks.

The number of weeks for which they drank tea:

`=52-6=46\; weeks`

1 pound of tea last 2 weeks.

Therefore, the number of pounds they drank:

`\begin{gathered} =(46)/(2) \\ =23\text{ pounds} \end{gathered}`

Since the tea costs $9.00 per pound, the amount spent:

`\begin{gathered} =23*9 \\ =\$207 \end{gathered}`

The couple spends about $207 on tea during the year.