QuestionDiane, Frank, and John served 102 orders total. If Diane served 10 more than Frank and John served 2 times Frank, find their orders.
Studdy Solution
STEP 1
Assumptions1. The total number of orders served by Diane, Frank, and John is102.
. Diane served10 more orders than Frank.
3. John served times as many orders as Frank.
STEP 2
Let's denote the number of orders served by Frank as . According to the problem, Diane served10 more orders than Frank, so we can denote the number of orders served by Diane as . John served2 times as many orders as Frank, so we can denote the number of orders served by John as .
STEP 3
Now, we can set up an equation to represent the total number of orders served by Diane, Frank, and John. The sum of the orders served by all three should be equal to the total number of orders, which is102.
STEP 4
implify the equation by combining like terms.
STEP 5
Subtract10 from both sides of the equation to isolate the term with .
STEP 6
Calculate the right side of the equation.
STEP 7
Divide both sides of the equation by4 to solve for .
STEP 8
Calculate the value of .
So, Frank served23 orders.
STEP 9
Now, we can find out how many orders Diane and John served by substituting into the expressions we found for them in Step2.
For Diane
STEP 10
Calculate the number of orders Diane served.
So, Diane served33 orders.
STEP 11
For John
STEP 12
Calculate the number of orders John served.
So, John served46 orders.
Number of orders Diane served33Number of orders Frank served23Number of orders John served46
Was this helpful?
