Answer:
The savings of Sid and Tim will be in 17:9 in 6 weeks.
Step-by-step explanation:
Initial savings of Sid = £ 13
Initial savings of Tim = £ 0
For each successive week Sid saved = £ 3.5
For each successive week Tim saved = £ 3
Let us assume that after "x weeks" the amounts of Sid and Tim are in ratio 17:9.
If Sid saves £ 3.5 in one week, in x weeks he will £ 3.5x. Since he had £ 13 initially, total amount he would have in x weeks will be £ (13 + 3.5x)
If Time saves £ 3 one week, in x weeks he will save £ 3x. Since, he didn't have any money initially, in x weeks he would have saved £ 3x
The ratio of their savings in x weeks would be 17:9
So,
Sid's saving : Tim's saving = 17 : 9
Using the values of expressions, we get:
[tex]13+3.5x:3x=17:9\\\\\frac{13+3.5x}{3x}=\frac{17}{9}\\\\ 9(13+3.5x)=17(3x)\\\\ 117+31.5x=51x\\\\ 117=51x-31.5x\\\\ 117=19.5x\\\\ x=\frac{117}{19.5}\\\\ x=6[/tex]
This means, the savings of Sid and Tim will be in 17:9 in 6 weeks.
The ratio of savings of Sid and Tim will be 17:9 in 6 weeks.
Given information:
Sid starts with savings of £13.
Tim starts with no savings.
Each week from now, Sid will save £3.50 and Tim will save £3.
Let, after x weeks, the ratio of savings of Sid and Tim will be 17:9.
After x weeks, the total saving of Sid will be,
[tex]S_s=13+3.5x[/tex]
After x weeks, the total saving of Tim will be,
[tex]S_t=0+3x=3x[/tex]
So, the value of x weeks can be calculated as,
[tex]\dfrac{S_s}{S_t}=\dfrac{17}{9}\\\dfrac{13+3.5x}{3x}=\dfrac{17}{9}\\9(13+3.5x)=17(3x)\\117+31.5x=51x\\19.5x=117\\x=6[/tex]
Therefore, the ratio of savings of Sid and Tim will be 17:9 in 6 weeks.
For more details, refer to the link:
https://brainly.com/question/15453016
