WRITTEN PROBLEMS INVOLVING EQUIVALENT RATIO
Q(i):- The ratio of profit to cost price on sales at DeeDee's is 3 : 5
Find the cost price of a skirt if the sales profit is £30?
First lets look at the question:-
First we have the ratio of profit to cost so we'll write this in ratio format P : C
Next the question tells us that it is in the ratio of 3 : 5
We have been asked to find the cost price and we've been told the profit is £30
A(i):-Therefore we can write the information we've been given as follows;
P : C
3 : 5
30 : ?
The 3 has turned into 30 so we will have to divide;
30 ÷ 3 = 10 (Now we must multiply the 5 X 10)
10 X 5 = 50
Therefore the cost price for the skirt is £50
(ii):- A type of concrete requires a mixture of sand, cement and grit in the ratio 4 : 1 : 2 , if 14 buckets of sand are used what are the quantities of cement and grit required?
We have the ratio of sand, cement and grit, so let's write this in ratio format
S : C : G
Next the question tells us these items are in the ratio of 4 : 1 : 2
We are told that 14 buckets of sand are used
We've been asked to find the quantities of cement and grit required
A(ii):-Therefore we can write the information we've been given as follows;
S : C : G
4 : 1 : 2
14 : ? : ?
We've went from 4 to 14 so we'll divide 14 ÷ 4 = 3.5(now we must multiply the 1 and the 2 by 3.5)
1 X 3.5 = 3.5 (cement)
2 X 3.5 = 7 (grit)
So to answer the question how much cement and grit is needed we see there is;
Cement 3.5 buckets and
Grit 7 buckets required.
NOW TO DIVIDE THE QUANTITIES IN A GIVEN RATIO:-
Q(i):- Divide £400 between John and Simon in the ratio 1 : 4
A(i):- J : S
1 : 4 = 5 parts
JOHN: 1/5 x 400 = £80 that is (400 ÷ 5 = 80)
SIMON: 4/5 x 400 = £320 that is ( 400 ÷ 5 = 80 then multiply the 80 x 4 = 320)
JOHN gets £80 and SIMON gets £320.
Q(ii):- The three angles in a triangle are in ratio 1 : 2 : 3, Find the size of each of the angles?
A(ii):- All the angles in a triangle add up to 180 degrees.
1 : 2 : 3 = 6 parts
Angles: the first angle we will look at is the 1 part out of the 6 parts, so as a fraction it would be 1/6 (one sixth)- therefore it will be 1/6 of the 180 degrees.
180 ÷ 6 = 30 degrees
The next angle is represented by the 2 parts out of the 6 parts, so as a fraction it would be 2/6(two sixths)which is equivalent to a 1/3(one third) - therefore this angle will be1/3 of the 180 degrees.
180 ÷ 3 = 60 degrees
The last angle is represented by the 3 parts out of the 6 parts, so as a fraction it would be 3/6 (three sixths) which is equivalent to a 1/2 ( a half ) - therefore this angle will be 1/2 of the 180 degrees.
180 ÷ 2 = 90 degrees
As an extra measure to check the sum of the degrees add them up;
30 + 60 + 90 = 180
Therefore the calculations are correct.
The size of the angles are 30 , 60 , and 90 degrees.
Q(iii):- A piece of rope is 60cm long and is cut into three pieces in the ratio 4 : 1 : 5
Find the length of the shortest piece?
A(iii):- 4 : 1 : 5 = 10 parts
The shortest piece is represented by the 1 part;
Therefore 1/10 x 60 = 6cms
The shortest piece is 6cms in length
More by this Author
What is a Matrix? A matrix is defined as an ordered rectangular array of numbers. They can be used to represent systems of linear equations. They are a key tool in linear Algebra. This ordered array...
ALGEBRA Here I intend to look at what is known as the nth term sequence. In doing so we will look at some examples and find the nth term which is known in mathematical terms by a "u" followed by a...
In this hub we are going to be looking at the different parts of a circle and how to calculate each of them. The Circumference of a Circle, this is the perimeter of a...