Answer :
Answer:
• 3 weeks
,• $207
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:
[tex]\frac{1}{x}+\frac{1}{6}=\frac{1}{2}[/tex]First, we solve for x:
[tex]\begin{gathered} \frac{1}{x}=\frac{1}{2}-\frac{1}{6} \\ \frac{1}{x}=\frac{3-1}{6} \\ \frac{1}{x}=\frac{2}{6} \\ 2x=6 \\ x=3\text{ weeks} \end{gathered}[/tex]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:
[tex]=52-6=46\; weeks[/tex]1 pound of tea last 2 weeks.
Therefore, the number of pounds they drank:
[tex]\begin{gathered} =\frac{46}{2} \\ =23\text{ pounds} \end{gathered}[/tex]Since the tea costs $9.00 per pound, the amount spent:
[tex]\begin{gathered} =23\times9 \\ =\$207 \end{gathered}[/tex]The couple spends about $207 on tea during the year.