Question

at joe's cafe 1 cup of coffee and 3 donuts is $4.10 and 2 cups of coffee and 2 donuts is $4.60, how much is 1 count? 1 cup of coffee?

Answer 1

c + 3d = 4.10.....multiply by -2
2c + 2d = 4.60
----------------
-2c - 6d = - 8.20 (result of multiplying by -2)
2c + 2d = 4.60
-----------------add
-4d = - 3.60
d = -3.60 / -4
d = 0.90 <==== cost of 1 doughnut

c + 3d = 4.10
c + 3(0.90) = 4.10
c + 2.70 = 4.10
c = 4.10 - 2.70
c = 1.40 <==== cost of 1 coffee

Answer 2

Cost of 1 cup of coffee=$ 1.4

and cost of 1 donut= $ 0.9

Explanation:

Let the cost of 1 cup of coffee is: $ x

and cost of 1 donut is: $ y

At joe's cafe 1 cup of coffee and 3 donuts is $4.10 and 2 cups of coffee and 2 donuts is $4.60.

i.e. we have:

x+3y=4.10

i.e. we have: x=4.10-3y---------(1)

and

2x+2y=4.60

Now, we put the value of x from equation (1) into this equation to get:

2(4.10-3y)+2y=4.60

2×4.10-6y+2y=4.60

⇒ 8.2-4y=4.60

⇒ 4y=8.2-4.60

⇒ 4y=3.6

⇒ y=3.6/4

⇒ y=0.9

and putting the value of y back in equation (1) we have:

x=4.10-3×0.9

⇒ x= 4.10-2.7

⇒ x=1.4