Question

write an algebraic expression for each of the given quantities. three brothers spent different amounts of money on their recent vacation. ethan spent $25 less than samuel. diego spent 3 times as much as ethan. how much did each brother spend when they spent a total of 3 times the amount samuel spent? let x represent the amount of money samuel spent. > enter the answer in each space provided. use numbers instead of words.

expression	money ethan spent	money diego spent

answer the question by writing and solving an equation. > enter the answer in each space provided. use numbers instead of words.
equation
samuel spent $, ethan spent $, and diego spent $.

Explanation:

Step1: Define expressions for each brother

Let $x$ = Samuel's spent amount.
Ethan's amount: $x - 25$
Diego's amount: $3(x - 25)$

Step2: Set up total spending equation

Total = 3×Samuel's amount:
$$x + (x - 25) + 3(x - 25) = 3x$$

Step3: Simplify and solve for $x$

Expand and combine like terms:
$$x + x - 25 + 3x - 75 = 3x$$
$$5x - 100 = 3x$$
$$2x = 100$$
$$x = 50$$

Step4: Calculate Ethan's spending

Substitute $x=50$:
$$50 - 25 = 25$$

Step5: Calculate Diego's spending

Substitute Ethan's amount:
$$3×25 = 75$$

Answer:

Expressions:

Money Ethan Spent: $x - 25$
Money Diego Spent: $3(x - 25)$

Equation:

$x + (x - 25) + 3(x - 25) = 3x$

Amounts:

Samuel spent $\$50$, Ethan spent $\$25$, and Diego spent $\$75$.