A school intended to buy a certain number of chairs for sh 16200. The supplier agreed to offer a discount of sh 60 per chair which enabled the school to get 3 more chairs.
Taking x originally intended number of chairs.
Write an expressions in term of x
Original price per chair
Price per chair after discount
Determine:
Number of chairs the school originally intended to buy;
Price per chair after discount;
Amount of money the school would have saved per chair if it bought the intended number of chairs at a discount of 15%
FAIRWINDS Credit Union - Best Credit Union in Central Florida
Let's break down the given information step by step:
Step 1: Writing expressions in terms of x:
Original price per chair: Since the school intended to buy x chairs for a total of sh 16200, the original price per chair can be calculated by dividing the total cost by the number of chairs:
Original price per chair = sh 16200 / x = sh (16200/x)
Price per chair after discount: The supplier offered a discount of sh 60 per chair, so the price per chair after discount can be calculated by subtracting the discount from the original price per chair:
Price per chair after discount = Original price per chair - Discount per chair = sh (16200/x) - sh 60 = sh ((16200 - 60x)/x)
Step 2: Determining the number of chairs the school originally intended to buy:
The supplier's discount of sh 60 per chair allowed the school to get 3 more chairs. So, the equation representing this relationship is:
Original number of chairs + 3 = x
To solve for x, subtracting 3 from both sides of the equation gives us:
Original number of chairs = x - 3
Step 3: Calculating the amount of money the school would have saved per chair if it bought the intended number of chairs at a discount of 15%:
The discount of 15% is equivalent to 15/100, or 0.15 of the original price per chair. So, the amount of money the school would have saved per chair can be calculated as:
Amount saved per chair = 0.15 * Original price per chair = 0.15 * (sh (16200/x))
However, since the original price per chair is sh (16200/x), we can substitute that in to simplify the expression:
Amount saved per chair = 0.15 * (sh (16200/x)) = sh (0.15 * (16200/x)) = sh (2430/x)
Therefore:
- The number of chairs the school originally intended to buy is x - 3.
- The price per chair after discount is sh ((16200 - 60x)/x).
- The amount of money the school would have saved per chair if it bought the intended number of chairs at a discount of 15% is sh (2430/x).
To solve this question, let's break it down step-by-step:
1. Expressions in terms of x:
- Original number of chairs intended to buy: x
- Original price per chair: Total amount of money divided by the number of chairs, which is 16200 / x
- Price per chair after discount: The original price per chair minus the discount of 60, so it becomes (16200 / x) - 60
2. Determine the number of chairs the school originally intended to buy:
Since the supplier offered a discount that allowed the school to get 3 more chairs, we can set up an equation:
(x + 3) * ((16200 / x) - 60) = 16200
We multiply the number of chairs by the price per chair after the discount to get the total cost, and set it equal to the initial total cost of 16200.
3. Determine the price per chair after discount:
The expression (16200 / x) - 60 gives us the price per chair after the discount.
4. Determine the amount of money the school would have saved per chair if it bought the intended number of chairs at a discount of 15%:
If the school bought the intended number of chairs at a 15% discount, they would have saved 15% of the original price per chair. So the amount saved per chair would be (15/100) * (16200 / x).
To find the specific values, you would need to solve the equation in step 2 for x, and then substitute the resulting value back into the expressions in step 1.
if the original price was p, then the total cost for x chairs was
xp = 16200
But, with the discount, 3 more chairs could be bought. That is,
(x+3)(p-60) = 16200
Now just work it out.
xp+3p-60x-180 = 16200
3p-60x = 180
p-20x = 60
but, we know that p = 16200/x, so
16200/x - 20x = 60
20x^2+60x-16200 = 0
x^2+3x-810 = 0
(x-27)(x+30) = 0
x = 27
Now you can work out the rest, I'm sure.