juice, bagel and coffee cost $2.40. the price of the juice will increase 50% and the price of the bagel will increase 20%, after, the same items cost $3.00

Question

Orange? juice, a raisin? bagel, and a cup of coffee from? Kelly's Koffee Kart cost a total of ?$2.40. Kelly posts a notice announcing? that, effective the following? week, the price of orange juice will increase? 50% and the price of bagels will increase? 20%. After the? increase, the same purchase will cost a total of ?$3.00?, and the orange juice will cost twice as much as coffee. Find the price of each item before the increase.

Answer 1

Okay, imagine that you represent the cost of orange juice with "x", the cost of a raisin bagel with "y", and the cost of a cup of coffee with "z". This would give you  x + y + z = $2.40 before the price changes. 

 

Now, after the price changes you know a few things:

 

• orange juice is now 50% more expensive so you can replace the original price "x" with "1.5x"
• bagels are now 20% more expensive so you can replace the original price "y" with "1.2y"
• coffee prices stayed the same so "z" stays "z"
• the new total cost is $3.00
• orange juice is now twice the cost of coffee so you can equate the new price of orange juice "1.5x" to the price of coffee "z" and get the equation "1.5x = 2z" or "0.75x = z"

So, your new equation for the cost of oj, a bagel, and a coffee is:

1.5x + 1.2y + z = $3.00

 

Since we know that z = 0.75x, we can replace z in the equation to get:

 

1.5x + 1.2y + 0.75x = $3.00  or  2.25x + 1.2y = $3.00

Solving for y you get:

1.2y = 3 - 2.25x   -->   y = 2.5 - 1.875x

 

 

Now, if we use the fact that z = 0.75x, we can substitute the original "x + y + z = 2.40" into "x + y + 0.75x = 2.40" and simplify that into "y = 2.40 - 1.75x"

 

 

Since we now have two equations for "y" we can set them equal to each other and solve for "x"

 

2.5 - 1.875x = 2.4 - 1.75x

0.1 = 0.125x

0.8 = x 

 

Now we know that "x", or the original price of orange juice, is $0.80

 

We can then plug in this value for x into the other equations we found to find the values for "y" and "z"

 

z = 0.75x

z = 0.75(0.80)

z = 0.60

 

x + y + z = 2.40

0.80 + y + 0.6 = 2.40

y = 2.40 - 1.40

y = 1

 

So now we know that

• x, or the original price for orange juice, is $0.80
• y, or the original price for a raisin bagel, is $1.00
• z, or the price for a coffee, is $0.60

 

Let me know if you're still having any issues understanding the problem!

Answer 2

Let j = price of juice

let b = price of bagel

let c = price of coffee

 

juice plus bagel plus coffe costs $2.40

equation 1)  j + b + c = 2.40

 

The price of juice will increase 50%

so bagel will now cost 1.5j

Price of bagel will increase 20% so

bagel now costs 1.2b

New cost is $3.00

equation 2). 1.5j + 1.2b + c = 3

 

at the new price juice costs twice as

much as coffee:

equation 3) 1.5j = 2c

 

replace 1.5j with 2c in equation 2

2c + 1.2b + c = 3

3c + 1.2b = 3

 

from equation 3 we have 1.5j=2c

1.5 = 1 1/2 = 3/2

(3/2)j= 2c

j = (2/3)(2c)

j = (4/3)c

 

in equation 1 replace j with (4/3)c

(4/3)c + b + c = 2.4

(4/3)c + (3/3)c + b = 2.4

(7/3)c + b = 2 4/10

(7/3)c + b = 2 2/5

(7/3)c + b = 12/5

clear the fractions by multiplying through by 15

15((7/3)c + b) = 15(12/5)

35c + 15b = 36

 

we now have 2 equations with 2 unknowns 

 

1)  3c + 1.2b = 3

2) 35c + 15b = 36

 

we can factor 3 out of each term in 1)

 

3(c + .4b) = 3

divide both sides by 3

c + .4b = 1

1)   c + .4b = 1

2) 35c + 15b = 36

----------------------

 

multiply 1) by -15 and 2) by .4

 

1) -15c - 6b = -15

2)  14c + 6b = 14.4

   ----------------------

     -c           = -.6

      c = .6

 

coffee is originally $.60

 

c + .4b = 1

.6 + .4b = 1

.4b = 1-.6

.4b = .4

b = 1

 

a bagel is originally $1.00

 

j+ b + c = 2.40

j + 1 + .6 = 2.4

j + 1.6 = 2.4

j = 2.4-1.6

j = .8

 

juice is originally $.80