Math

QuestionElsa, Chau, and Manuel served 105 orders total. Elsa served 5 more than Chau, and Manuel served 3 times Chau. Find their orders.

Studdy Solution

STEP 1

Assumptions1. The total number of orders served by Elsa, Chau, and Manuel is105. . Elsa served5 more orders than Chau.
3. Manuel served3 times as many orders as Chau.

STEP 2

Let's denote the number of orders Chau served as x. Therefore, the number of orders Elsa served is x +5, and the number of orders Manuel served isx.

STEP 3

We know that the total number of orders is105. So, we can write the equation as followsx+(x+5)+3x=105x + (x +5) +3x =105

STEP 4

implify the equation by combining like terms.
x+=105x + =105

STEP 5

Subtract5 from both sides of the equation to isolate the term with x.
5x=10555x =105 -5

STEP 6

Calculate the right side of the equation.
5x=1005x =100

STEP 7

Divide both sides of the equation by5 to solve for x.
x=1005x = \frac{100}{5}

STEP 8

Calculate the value of x.
x=20x =20So, Chau served20 orders.

STEP 9

Now, let's find the number of orders Elsa served. We know that Elsa served5 more orders than Chau.
lsasorders=x+5lsa's\, orders = x +5

STEP 10

Plug in the value of x into the equation.
lsasorders=20+5lsa's\, orders =20 +5

STEP 11

Calculate the number of orders Elsa served.
lsasorders=25lsa's\, orders =25So, Elsa served25 orders.

STEP 12

Finally, let's find the number of orders Manuel served. We know that Manuel served times as many orders as Chau.
Manuelsorders=xManuel's\, orders =x

STEP 13

Plug in the value of x into the equation.
Manuelsorders=3times20Manuel's\, orders =3 \\times20

STEP 14

Calculate the number of orders Manuel served.
Manuelsorders=60Manuel's\, orders =60So, Manuel served60 orders.
Number of orders Elsa served25Number of orders Chau served20Number of orders Manuel served60

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