A grocer bought sugar worth of 4500. He sold one-third of it at a pain of 10%. At what gain
1 answer:
Answer:
13%
Step-by-step explanation:
the cost price of 1/3 of the sugar = 1/3 x 4500 = 1500
gain= x 100
let x = unknown selling price
(x - 1500) / 1500 = 0.1
to solve for x, multiply both sides of the equation by 1500
x - 1500 = 150
x = 1650
the selling price of the 1/3 of sugar that yielded a 10% gain is 1650
to determine the gain percent of the remaining sugar, the selling price of the remaining sugar has to be determined . Let the selling price be represented by a
Based o the information in the question and the previous solution, the following equation can be derived
{(a + 1650) - 4500} / 4500 = 0.12
Solve for a
Multiply both sides of the equation by 4500
a + 1650 - 4500 = 540
a = 3390 = selling price of 2/3 of the sugar
Percent gain that the 2/3 of the sugar should be sold can be determined by taking the following steps
first find cost price of the 2/3 of sugar = 2/3 x 4500 = 3000
gain = (3390 - 3000) /3000 = 0.13 = 13%
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Answer:
Between 150 and 450
Step-by-step explanation:
We are going to find the number by resolving a system of linear equations.
First we write the system equations :
Where C : children, S : students and A : adults
The equation represents the ''full attendance''
The second equation :
This equation represents the totaled receipts.
The system :
has the following associated matrix :
By performing elementary matrix operations we find that the matrix is equivalent to
The new system :
Working with the equations :
Our solution vector is :
For example :
If 0 adults attended ⇒ A = 0
This verify the totaled receipts equation :
150($3)+600($5) = $ 3450
A ≥ 0 ⇒ If A = 0 ⇒ C = 150
C = 150 is the minimum children attendance
From the equation :
S ≥0
600 - 2A ≥ 0
600 ≥ 2A
300≥ A
A is restricted to the interval [ 0, 300]
When A = 0 ⇒ C = 150
When A = 300 ⇒C = 150 + A = 150 + 300 = 450
Children ∈ [ 150,450]
With C being an integer number (including 0)
Also S and A are integer numbers (including 0)