Question

write an algebraic expression for each of the given quantities.
three waiters at a local restaurant earned different amounts of money the past week. emma earned $40 less than twice the amount daniel earned. juan earned $60 more th
daniel.
how much did each waiter earn when they earned a total of 250 more than 3 times what daniel made? let x represent the amount of money daniel earned.

enter the answer in each space provided. use numbers instead of words.

	expression
money juan earned

answer the question by writing and solving an equation.

enter the answer in each space provided. use numbers instead of words.

equation

daniel earned $ , emma earned $ , and juan earned $ .

Explanation:

Step1: Define Emma's earnings

Let $x$ = Daniel's earnings. Emma earned $40 less than twice Daniel's earnings.
Expression: $2x - 40$

Step2: Define Juan's earnings

Juan earned $60 more than Daniel.
Expression: $x + 60$

Step3: Set up total earnings equation

Total earnings equal 250 more than 3 times Daniel's earnings. Sum of all three earnings: $x + (2x - 40) + (x + 60) = 3x + 250$

Step4: Simplify left side of equation

Combine like terms: $x + 2x + x - 40 + 60 = 4x + 20$
Equation becomes: $4x + 20 = 3x + 250$

Step5: Solve for $x$

Subtract $3x$ from both sides: $4x - 3x + 20 = 250$
Simplify: $x + 20 = 250$
Subtract 20 from both sides: $x = 250 - 20 = 230$

Step6: Calculate Emma's earnings

Substitute $x=230$ into Emma's expression: $2(230) - 40 = 460 - 40 = 420$

Step7: Calculate Juan's earnings

Substitute $x=230$ into Juan's expression: $230 + 60 = 290$

Answer:

Expressions:

Money Emma Earned: $2x - 40$
Money Juan Earned: $x + 60$

Equation:

$4x + 20 = 3x + 250$

Earnings:

Daniel earned $\$230$, Emma earned $\$420$, and Juan earned $\$290$