# WRITTEN PROBLEMS INVOLVING EQUIVALENT RATIO

## Problem Solving

**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 be

^{}

^{1}/_{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

**- therefore this angle will be**

^{1}/_{2 }( a half )

^{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**

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