Lesson: How Many Variables to Assign

Cost per person = (total cost)/(number of people)

Let x = total cost to charter the aircraft

Word equation: (cost per person with 36 people) = (cost per person with 40 people) + 12

We get: x/36 = x/40 + 12

To eliminate the fractions, multiply both sides by 360 (the least common multiple of 36 and 40)

We get: 10x = 9x + 4320

Solve: x = 4320

a) what is the fixed cost to charter the aircraft?
Answer = $4320

b) what is the cost person if 40 people charter the aircraft?
Answer = $4320/40 = $108

ASIDE: the cost person if 36 people charter the aircraft = $4320/36 = $120

Hi anisap,

For this question, I decided to express the costs in terms of CENTS. So, rather than say the cost of the apples is 0.75A (dollars), I said the cost of the apples is 75A (cents)

It doesn't make any difference whether we write our expressions in terms of cents or dollars. HOWEVER, we must be consistent.
That is, we can't express the cost of the apples in DOLLARS, 0.75A, and then express the cost of the bananas in CENTS, 50(20 - A).

To demonstrate that it doesn't matter whether we use dollars or cents, let's solve the question in terms of DOLLARS

If A = the NUMBER of apples,
then 20 - A = the NUMBER of bananas.

So, 0.75A = the COST of the apples (in dollars)
And 0.50(20 - A) = the COST of the bananas (in dollars)

We can now write: 0.75A + 0.50(20 - A) = 13.00
Expand: 0.75A + 10 - 0.5A = 13.00
Simplify: 0.25A + 10 = 13
Subtract 10 from both sides to get: 0.25A = 3
Solve, A = 12
This means Lila bought 12 apples.
It also means Lila bought 8 bananas (since she bought a total of 20 pieces of fruit)

ASIDE: Once we have the equation 0.75A + 0.50(20 - A) = 13.00, we choose to eliminate the decimals by multiplying both sides of the equation by 100.
When we do this, we get the EQUIVALENT equation 75A + 50(20 - A) = 1300, which is the same equation we got in the video.

Does that help?

Cheers,
Brent

Be careful. Reaching the correct answer with that approach was a coincidence.

If 1 apple COSTS 1.5 as much as 1 banana, we can write the following ratio:
(COST per apple)/(COST per banana) = 1.5/1 (or just 1.5)

However, the 20 doesn't refer to the total COST of the bananas and apples. The 20 refers to the total NUMBER of bananas and apples.

As such, we can't use that approach.

Notice that your approach will always lead to the same solution (12 apples and 8 bananas) regardless of the total cost of the 20 pieces of fruit.

For example, if the total cost of the 20 pieces of fruit were $16, then that would mean Lila bought 16 apples and 4 bananas

If the total cost of the 20 pieces of fruit were $12.50, then that would mean Lila bought 10 apples and 10 bananas.

etc.

Cheers,
Brent

Here are the two equations we're starting with:
(1) 75A + 50B = 1300
(2) A + B = 20

First notice that I didn't have to take equation (1) and divide both sides by 25.
I could have just taken equation (2) and multiplied both sides by 50 to get:
(1) 75A + 50B = 1300
(2) 50A + 50B = 1000
From here, we would just subtract (2) from (1) to get: 25A = 300, which means A = 12

HOWEVER, instead of working with such big numbers, I decided to first simplify equation (1) by dividing both sides of the equation by 25 to get:
(1) 3A + 2B = 52
(2) A + B = 20

From here, I recognized that we can (eventually) eliminate the variable B, by multiplying both sides of equation B by 2 to get:
(1) 3A + 2B = 52
(2) 2A + 2B = 40
Since we have 2B in both equations, we can eliminate the variable B by subtracting (2) from (1) to get:
A = 12

So, as you can see, there are many different ways to solve this system of equations.