Algebra problem?

Question

At a fundraiser breakfast, the bill for three glasses of orange juice and five pancake specials is $7.60, whereas the bill for five glasses of orange juice and four pancake specials is $7.90. What would be the bill for one glass of orange juice and one pancake special?

Answer 1

let x be the orange juice and y the pancakes

3x + 5y = 7.6------(1)

5x + 4y = 7.9------(2)

(1) * -5/3=> -5x - 25/3 y = -12.6667
(1) + (2) => 0x + 4y - 25/3y= -12.6667 + 7.9 = - 4.7667

-4.3334y = -4.7667
y= 1.10 $ the pancake
x = 0.70 $ the orange juice

Answer 2

Let x = price of the orange juice and y = price of pancakes

3x + 5y = 7.60

5x + 4y = 7.90
Need to eliminate one of the variables:

multiply the first eqn by 5 and the second by 3

15x + 25y = 38

15x + 12y = 23.7 Subtract the second from the first

13y = 14.3

y= 1.10 so pancakes are 1.10

substitute y into equation 1 or 2

3x + 5(1.10) = 7.60

3x + 5.50 = 7.60

3x = 7.60 - 5.50

3x = 2.10

x= 0.70 so orange juice is 0.70

Answer 3

o = orange
p = pancake

i) 3 o + 5 p = 7.60
ii) 5 o + 4 p = 7.90

i) 3 o = 7.60 - 5p
o = (7.60 - 5p)/3

ii)
5(7.60 - 5p)/3 + 4p = 7.90
mmc(3 and 1) = 3
38,00 - 25p + 12p = 23.70
-13p = 23,70 - 38.00
-13p = -14.30
p = 14.30/13
p = $1.10

3 o + 5p = 7.60
3 o + 5(1.10) = 7.60
3 o = 7.60 - 5.50
3 or = 2.10
or = 2.10 : 3
or = $.70
Answer: The bill for one glass of orange juice and one pancake special would be $.70 and $1.10, respectively.
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Answer 4

you need to start by turning them both in to a formula,
eg. 3j + 5p = 7.60 and 5j + 4 p = 7.90

now change the first one so you get p = 1.52 - (3j/5)

substitute this into the 2nd one so you get,

5j + 4 ( 1.52 - (3j/5)) = 7.90

now you only have one variable so solve for j.
use you answer in the p = 1.52 - (3j/5) to get a value for p
now substitue both values into the original formulae to check them :D good luck.

Answer 5

Orange Juice = x
Pancake Special = y

3x + 5y = 7.6
5x + 4y = 7.9

Use substitution:

4y = 7.9 - 5x

y = (7.9 - 5x)/4

So:

3x + 5(7.9 - 5x)/4 = 7.6

Answer 6

3OJ+5P=7.60
5OJ+4P=7.90
OJ=(7.90-4P)/5 (substitute this back to 1st eq. for OJ)
3(7.90-4P)/5+5P=7.60
(23.7-12P)/5 + 5P = 7.60
(23.7-12P)/5=7.60-5P
23.7-12P=5(7.60-5P)
23.7-12P=38-25P
25P-12P=38-23.7
13P=14.3
P=1.10
OJ=.70