Question

9. AMUSEMENT PARKS Nick goes to the amusement park to ride roller coasters, bumper
cars, and water slides. The wait for the roller coasters is 1 hour, the wait for the
bumper cars is 20 minutes long, and the wait for the water slides is only 15 minutes
long. Nick rode 10 total rides during his visit. Because he enjoys roller coasters the
most, the number of times he rode the roller coasters was the sum of the times he rode
the other two rides. If Nick waited in line for a total of 6 hours and 20 minutes, how
many of each ride did he go on?

Answer 1

Answer:

he rode the roller coaster 4 times the bumper cars 3 times and the water slide 4 hoped i helped

Step-by-step explanation:

Answer 2

The question is an illustration of a system of simultaneous equation

He rode the roller coaster 5 times; bumper cars 1 time and water slides 4 times.

Let:

$b \to$ bumper cars

$r \to$ roller coaster

$w \to$ water slides

He rode 10 total rides.

So:

$b + r + w = 10$

The equation for the times he waited is:

$r + \frac{20}{60}b + \frac{15}{60}w = 6\frac{20}{60}$

Simplify fraction

$r + \frac b3 + \frac w4 = 6\frac 13$

The proportion of rides is:

$r =b + w$

Substitute $r =b + w$ in $b + r + w = 10$ and $r + \frac b3 + \frac w4 = 6\frac 13$

$b + b + w + w = 10$

$2b + 2w = 10$

Divide through by 2

$b + w = 5$

Similarly

$r + \frac b3 + \frac w4 = 6\frac 13$

$b + w + \frac b3 + \frac w4 = \frac{19}3$

Multiply through by 12

$12b + 12w + 4b + 3w = 4 \times 19$

$16b + 15w = 76$

Make b the subject in $b + w = 5$

$b = 5 -w$

Substitute $b = 5 -w$ in $16b + 15w = 76$

$16(5 -w) + 15w = 76$

$80 -16w + 15w = 76$

Collect like terms

$-w = 76 - 80$

$-w = -4$

$w = 4$

Recall that:

$b = 5 -w$

$b = 5 - 1$

$b =4$

Recall that:

$r =b + w$

$r = 1 + 4$

$r = 5$

Hence, he rode the roller coaster 5 times; bumper cars 1 time and water slides 4 times.

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