Question

Sarah, Natasha and Richard share some sweets in the ratio 4:2:3. Sarah gets 13 more sweets than Richard. How many sweets are there altogether?

Answer 1

117 sweets

Solution,

Given ratio= 4 : 2 : 3

Sarah has 4x sweets.

Natasha has 2x sweets.

Richard has 3x sweets.

Given,

`3x + 13 = 4x \\ 3 x - 4 x= - 13 \\ - x = - 13 \\ x = 13`

Now,

Total sweets:

`4x + 2x + 3x \\ = 4 * 13 + 2 * 13 * 3 * 13 \\ = 52 + 26 + 39 \\ = 117 \: sweets`

Hope this helps..

Good luck on your assignment...

Answer 2

117 sweets

Explanation:

Please see attached picture for full solution. (model method)

S, N and R represents the number of sweets Sarah, Natasha and Richard have respectively.

Alternatively,

Let the number of sweets Sarah have be 4x.

Number of sweets Natasha have= 2x

Number of sweets Richard have= 3x

Sarah gets 13 more sweets than Richard

4x= 3x +13

4x -3x= 13

x= 13

Total number of sweets

= 4x +2x +3x

= 9x (simplify)

= 9(13) (subst. x=13)

= 117 sweets