math

[halo]

Luna is examining the finance sector.
She finds that the number of days when the cashier was ill is 5/2 times more than the number of days when the accountant was ill.
The number of days when the accountant has been ill is 2/3 of the number of days of the financier.
In total they have been sick for 10 days.
How many days has each been sick?

 

[JeffM]

This is a help site rather than an answer site.

What have you tried?

Do you know algebra?

Do you see that the answers must be whole numbers?

 

[halo]

c=cashier a=accountant f=financier
c = 5/2 a
a
a = 2/3 f or f = 3/2 a

Summed they equal 10 days

5/2 a + a + 3/2 a = 10
10/2 a = 10
5a = 10
a = 2
I did it for the first time but I want to know if this is the right way?

 

[JeffM]

Perfect except for one thing. You did not check your answers.

[MATH]a = 2 \text { and } c = \dfrac{5a}{2} = \dfrac{5 * 2}{2} = 5, \text { a whole number. } \checkmark[/MATH]
[MATH]a = 2 \text { and } f = \dfrac{3a}{2} = \dfrac{3* 2}{2} =3,\text { a whole number. } \checkmark[/MATH]
[MATH]2 + 5 + 3 = 7 + 3 = 10. \ \checkmark[/MATH]

 

[halo]

Perfect except for one thing. You did not check your answers.

[MATH]a = 2 \text { and } c = \dfrac{5a}{2} = \dfrac{5 * 2}{2} = 5, \text { a whole number } \checkmark[/MATH]
[MATH]a = 2 \text { and } f = \dfrac{3a}{2} = \dfrac{3* 2}{2} =3,\text { a whole number } \checkmark.[/MATH]
[MATH]2 + 5 + 3 = 7 + 3 = 10. \ \checkmark[/MATH]

thank you