Solve ratio and proportion problems using the unitary method
Information: Unitary Method - Methods for solving ratio and proportion questions
If three Mars bars cost 90p, how much do five of them cost?
Without doing much thinking, you’ll probably easily arrive at the answer of £1.50. The problem is the ‘without much thinking’ part. We need to look at what you actually did there.
Well, three bars cost 90p, that means one bar must cost 30p. You then said fives bars will cost 5 x 30p = £1.50.
We can use this method to solve problems involving ratios.
It’s called the unitary method, because what you’re doing is working out the value of a single unit in order to solve the problem.
Application Unitary Method:
Instead, say I told you Hannah and Emily buy chocolate bars in the ratio 3:5. Hannah spends £2.70 on her chocolate. How much does Emily spend?
The only difference is that we’re not told anything about how many bars they’re each buying. Yet, despite this, we can still work out the money Emily spends on the chocolate. This is actually what makes ratios so powerful – without knowing everything about a situation, we can still discover new information.
The process is the same – Emily purchased 5 ‘parts’ of chocolate, of every 3 ‘parts’Hannah bought.
Hannah’s total came to £2.70, and she bought 3 parts.
1) So we divide £2.70 by 3 to work out the value of just 1 part (the unit)
£2.70 / 3 = 90p
2) Now since Emily bought 5 parts of chocolate, we multiply one part by 5, and get
90p x 5 = £4.50 which is our Final Answer, which we found by using the ratio- proportion method. (Unitary Method)
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