Question

Amy and Ben share £21 between them in the ratio 5 : 2. How much does Amy get?

(Im really sorry I just don't understand ratio.)

Answer 1

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`\underline{ \underline{ \sf{First ,\: Let's \: learn \: about \: the \: ratio}}} :`

Let us consider , there are 30 boys and 40 girls in a school. So, the ratio of number of boys to number of girls =
`\sf{ (30)/(40) = (3)/(4) = 3:4}` and read as 3 is to 4. We can say , the ratio compares two of more quantities of same unit. Until two quantities have same units , it is meaningless to compare by ratio. So, to find the ratio of two quantities , it is necessary to express them in same unit or of same kind. Since , they are in division form. So ,ratio is unit less quantity. Thus , the ratio is a comparison of two quantities of the same kind in division which doesn't have any units. For example :
`\sf{ (a)/(b)}` is a ratio and is read as ' a is to b ' in which ' a : is antecedent and ' b ' is called consequent.

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`\underline{ \underline{ \sf{Now \: let's \: solve : }}}`

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`\underline{ \sf{Solution}} :`

£ 21 is to be divided between Amy and Ben in the ratio 5 : 2. So, let Amy get £ 5x and Ben get £ 2x.

Then , According to the question ,
`\text{5x +2x = 21}`

Solve for x :

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`\sf{7x = 21}`

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`\sf{ (7x)/(7) = (21)/(7) }`

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`\sf{x = 3}`

The value of x is 3. Now , substitute the value of x in 5x :

Amy received £ 5x = 5 × 3 = £ 15 .

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`\boxed{ \boxed{ \tt{Our \: final \: answer \: is \bold{£ \: 15}}}}`

Hope I helped ! ツ

Have a wonderful day / night ♡

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