Math Problem?

Question

Tanisha and Rachel had lunch at the mall. Tanisha ordered three slices of pizza and two colas. Rachel ordered two slices of pizza and three colas. Tanisha's bill was $6.00, and Rachel's bill was $5.25.

What was the price of one slice of pizza? $

What was the price of one cola? $

Answer 1

eq 1: 2p+3c=5.25
eq 2: 3p+2c=6
___________
solve eq 2 for c:
c=(6-3p)/2

plug c into eq 1
______________
2p+3(6-3p)/2=5.25

distribute the 3: 2p+(18-9p)/2=5.25
x both sides by 4: 8p+2(18-9p)=21
dist the 2: 8p+36-18p=21
-10p=21-36
-10p=-15
p=1.5

a slice of pizza costs a buck fiddy.

Plug p into eq2 and solve for c--that will be the price of cola.

Answer 2

set cola=c and pizza=p
then, use what you know from the problem to make equations. namely, the fact that tanisha's 3 slices of pizza and 2 colas totaled $6 and rachel's 2 slices of pizza and 3 colas total $5.25

tanisha: 3p+2c = $6.00
rachel: 2p+3c = $5.25

solve for these two expressions in whatever way you are comfortable with.

Answer 3

$6.00 = 3 slices + 2 colas ;; equation [1]
$5.25 = 2 slices + 3 colas ;; equation [2]

subract the equations [1] - [2]::

$0.75 = 1 slices - 1 cola

Therefore a slice costs 75 cents more than a cola.

1 slice = 1 cola + $0.75
2 slice = 2 cola +$1.50 ;; equation 3

Substitute equation 3 into equation 2:

$5.25 = (2 colas +$1.50) + 3 colas

subtract $1.50 from both sides:

$5.25 - $1.50 = 2 colas + 3 colas
$3.75 = 5 colas.
$3.75 / 5 = 1 colas
1 cola = $0.75

We found before that 1 slice = $0.75 + cola
so:
1 slice = $0.75 + $0.75
1 slice = $1.50

Answer 4

T > 3P + 2C = 6
R > 2P + 3C = 5.25

3P = 6 - 2C
P = (6 - 2C)/3

2/3(6 - 2C) + 3C = 5.25
4 - 4/3 C + 9/3 C = 5.25
5/3 C = 1 1/4 = 5/4
C = 5/4 * 3/5 = 15/20 = 3/4 = .$0.75 = COKE

3P + 2(.75) = 6
3P + 1.5 = 6
3P = 4.5
P = $1.50 = PIZZA

Answer 5

let pizza price = $ p
cola price = $ c
3p + 2c = 6
2p + 3c = 5.25

-6p - 4c = - 12
6p + 9c = 15.75----Now add

5c = 3.75
c = 0 . 75
3p + 1.5 = 6
3p = 4.5
p = 1.5
One slice of pizza: $1.50
One cola: $ 0.75

Answer 6

One slice of pizza costs $1.50 and one cola costs $0.75.

Answer 7

3p + 2c = 6
2p + 3c = 5.25

solve for p or c in one equation, and than substitute into the other.

cola: c=0.75
pizza: p=1.5

Answer 8

let cola be y and pizza be x
3x+2y = 6
2x+3y = 5.25

x = (6-2y)/3
x = (5.25-3y)/2
12-4y=15.75-9y
5y=3.75
y=.75
3x+2(.75)=6
x=1.5