Members of the Wide Waters Club pay

Mathematics

1 answer:

vivado [14]3 years ago

6 0

Answer:

The number of times members and non-members will have to rent a boat in order to pay the same amount=20

Step-by-step explanation:

We can have two expressions to show the total cost paid by a member and non-member;

Total cost by member=Cost per summer season+cost per number of times they rent a boat×number of times they rent a boat

where;

Cost per summer season=$105

Cost per number of times they rent a boat=$9.50

Number of times they rent a boat=n

Replacing;

Total cost by a member=105+(9.5×n)=9.5 n+105......equation 1

Total cost by a non-member=Cost per number of times they rent a boat×number of times they rent a boat

where;

Cost per number of times they rent a boat=$14.75

Number of times they rent a boat=n

Replacing;

Total cost by a non-member=(14.75×n)=14.75 n......equation 2

To calculate the number of times they would have to rent a boat in order to pay the same amount, we equate equation 1 to equation 2

9.5 n+105=14.75 n

14.75 n-9.5 n=105

5.25 n=105

n=105/5.25

n=20

The number of times members and non-members will have to rent a boat in order to pay the same amount=20

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belka [17]

In the figure below

1) Using the theorem of similar triangles (ΔBXY and ΔBAC),

$\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}$

Where

$\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}$

Thus,

$\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}$

thus, BC = 7.5

2) BX = 9, BA = 15, BY = 15, YC = y

In the above diagram,

$\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}$

Thus, from the theorem of similar triangles,

$\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}$

solving for y, we have

$\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}$

thus, YC = 10.