Question

Sheldon’s and Sam’s salaries are in the ratio 6:11. If Sheldon earns $540, how much does Sam earn?

Answer 1

Given:

• Sheldon’s and Sam’s salaries are in the ratio 6:11.

• Sheldon earns $540.

To calculate:

• How much does Sam earn?

Calculation:

Let the salaries earned by Sheldon be 6x and by Sam be 11x respectively.

According to the question,

→ Sheldon earnings = $ 540

→ 6x = 540

→ x = $\sf { \cancel{\dfrac{540}{6}}}$

→ x = 90

Therefore,

→ Sam earnings = 11x

→ Sam earnings = $ ( 11 × 90 )

→ Sam earnings = $ 990

Therefore, Sam earns $ 990.

Verification :

As we found that,

• Sheldon earns $540
• Sam earns $ 990

So,

Ratio of Sheldon’s and Sam’s salaries = 6 : 11

We can also write it antedecant and consequent in fraction ::

→ $\sf \purple { \dfrac{6}{11} }$

Now, it is in simplest form.

According to the question,

→ $\sf { \dfrac{540}{990} = \dfrac{6}{11} }$

LHS :

→ $\sf { \dfrac{540}{990} }$

Divide the numerator and the denominator by 10.

→ $\sf { \dfrac{54}{99} }$

Divide the numerator and the denominator by 9.

→ $\sf \purple { \dfrac{6}{11} }$

RHS:

→ $\sf \purple { \dfrac{6}{11} }$

LHS = RHS,

Hence, verified!

Answer 2

Let the income of Sheldon and Sam be 6x and 11x respectively.

∴ 6x = 540

⇒ x = 90.

∴ 11x = 90 · 11 = 990.

Therefore, the income of Sam is $990.