During her holiday, hannah rent a bike
She pays a fixed cost of $8 and then a cost of $4.50 per day
Hannah pays with a $50 note and receives $10.50 change.
Calculate for how many days Hannah rents the bike ( simultaneous equation ) plz explain also
"simultaneous equation" would be overkill here, just do some arithmetic
actual cost = 50-10.50 = $39.50
less the fixed $8 cost = 31.50
number of days = 31.50/4.50 = 7
Cost = 4.5x + 8.
50-10.5 = 4.5x + 8.
X = 7 days.
How to do this in simultaneous method ?
Well, let's assume that Hannah rents the bike for "x" number of days.
We can set up two equations to represent the given information:
1. The total cost equation:
Total cost = Fixed cost + (Cost per day * Number of days)
Total cost = $8 + ($4.50 * x)
2. The change equation:
Change = Amount paid - Total cost
$10.50 = $50 - ($8 + $4.50 * x)
To solve this system of equations, we'll start by simplifying the second equation:
$10.50 = $50 - ($8 + $4.50 * x)
$10.50 = $50 - $8 - $4.50 * x
$10.50 = $42 - $4.50 * x
We'll now bring the terms involving 'x' to the left side:
$4.50 * x = $42 - $10.50
$4.50 * x = $31.50
Finally, we'll divide both sides by $4.50 to solve for 'x':
x = $31.50 / $4.50
x ≈ 7
So, Hannah rents the bike for approximately 7 days.
To solve this problem using simultaneous equations, let's assume that Hannah rented the bike for "x" number of days.
Given that she paid a fixed cost of $8 and then a cost of $4.50 per day, we can write the following equations:
1) Total cost of rental = Fixed cost + Cost per day multiplied by the number of days
Total cost = 8 + 4.50x
2) Change received = Amount paid - Total cost of rental
Change received = 50 - (8 + 4.50x)
We know that Hannah received $10.50 in change, so we can equate the second equation to 10.50:
50 - (8 + 4.50x) = 10.50
Now let's solve this equation to find the value of x (the number of days):
50 - 8 - 4.50x = 10.50
42 - 4.50x = 10.50
To isolate x, we'll subtract 42 from both sides:
-4.50x = 10.50 - 42
-4.50x = -31.50
Finally, divide both sides by -4.50 to solve for x:
x = -31.50 / -4.50
x = 7
Therefore, Hannah rented the bike for 7 days.