# Question #0efd8

Oct 21, 2017

They have 56 sweets altogether.

#### Explanation:

Let :

n= the number of sweets Nurul has
s= the number of sweets Sam has
r= the number of sweets Rebecca has

From the problem, we can say the $n = s + 8$ since it says the Nurul has 8 more sweets than Sam.

Similarly, we can also say the $n = \frac{5}{3} s$ since the ratio between the number of sweets Nurul has compared to Sam is a 5:3 ratio.

Substitute and solve for s:

$\frac{5}{3} s = s + 8$

$\frac{5}{3} s = \frac{3}{3} s + 8$

$\frac{5}{3} s - \frac{3}{3} s = \frac{3}{3} s + 8 - \frac{3}{3} s$

$\frac{2}{3} s = 8$

$2 s = 24$

$s = 12$

Now use $n = s + 8$ to find the number of sweets Nurul has:

$n = s + 8$
$n = 12 + 8$
$n = 20$

Finally, find the number of sweets Rebecca has. Rebecca has a 6:3 ratio in sweets compared to Sam. 6:3 simplified is 2:1 so Rebcca has 2 times as many sweets as Sam.

$r = 2 s$
$r = 2 \cdot 12$
$r = 24$

So, the total number of sweets is all the sweets of every person combined or in other words:

Total number of sweets= n+s+r

$12 + 20 + 24 = 56$

They have 56 sweets altogether. I hope this helps!