Teresa, charlie, and justin served a total of 153 orders monday at the school cafeteria. justin served 4 times as many orders as charlie. teresa served 9 more orders than charlie. how many orders did they each serve?

Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders

Solution:

Let "a" be the orders served by Teresa

Let "b" be the orders served by Charlie

Let "c" be the orders served by Justin

Teresa, Charlie, and Justin served a total of 153 orders

Therefore,

a + b + c = 153 eqn 1

Justin served 4 times as many orders as Charlie

Orders served by Justin = 4( orders served by Charlie )

c = 4b eqn 2

Teresa served 9 more orders than Charlie

orders served by Teresa = 9 + orders served by Charlie

a = 9 + b eqn 3

Let us solve eqn 1 and eqn 2 and eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

9 + b + b + 4b = 153

9 + 6b = 153

6b = 153 - 9

6b = 144

b = 24

Substitute b = 24 in eqn 3

a = 9 + 24

a = 33

Substitute b = 24 in eqn 2

c = 4(24)

c = 96

Thus Teresa served 33 orders and Charlie served 24 orders and Justin served 96 orders

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

i got 10.28 but that rounds up to 10.3