Question

Ashley, Bob, and Scott have a total of $95 in their wallets. Scott has 3 times what Bob has. Ashley has $5 less than Bob. How much does each have?

Answer 1

Step-by-step explanation:

As per the provided information in the given question, we have :

• Ashley, Bob, and Scott have a total of $95 in their wallets.
• Scott has 3 times what Bob has.
• Ashley has $5 less than Bob.

We are asked to calculate how much does each have.

― Let us suppose the share of Bob as x. According to the question, Scott has 3 times what Bob has. Writing the expression of the share of Scott in the terms of Bob's share :

$\longrightarrow \sf{\quad { Scott's \; share = 3x}}$

Also, according to the question, Ashley has $5 less than Bob. Writing the expression of the share of Ashley in the terms of Bob's share :

$\longrightarrow \sf{\quad { Ashley's \; share = (x - 5) }}$

Now, we have been given in the question that Ashley, Bob, and Scott have a total of $95 in their wallets. So, according to this statement we can conclude that the sum of the share of Ashley, Bob, and Scott will be $95. Writing it in the form of a linear equation,

$\longrightarrow \sf{\quad { (x - 5) + x + 3x = \ \; 95 }}$

Remove the brackets in the LHS.

$\longrightarrow \sf{\quad { x - 5 + x + 3x = \ \; 95 }}$

Performing addition of the like terms in LHS.

$\longrightarrow \sf{\quad { - 5 + 5x = \ \; 95 }}$

Transposing – 5 from LHS to RHS, its sign will get changed.

$\longrightarrow \sf{\quad {5x = \ \; 95 + 5 }}$

Performing subtraction in RHS.

$\longrightarrow \sf{\quad {5x = \ \; 100 }}$

Transposing 5 from LHS to RHS, its arithmetic operator will get changed.

$\longrightarrow \sf{\quad {x = \ \; \cancel{\dfrac{100}{5}} }}$

Dividing 100 by 5.

$\longrightarrow \quad { \textbf{\textsf{x}} = \sf \ \; \textbf{\textsf{20}} }$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

• Ashley's Share : (x – 5) = $(20 – 5) = $15
• Bob's Share : x = $20
• Scott's Share : 3x = $ 3(20) = $60