Question

Paul paid $25.50 for 3 cups of hot chocolate and 4 cups of hot tea. The cost of each cup of tea was 2/3 the cost of each cup of hot chocolate. How much did each cup of hot chocolate cost?

Answer 1

Answer: Each cup of hot chocolate cost $4.5

Step-by-step explanation:

Let be "c" the cost of each cup of hot chocolate and "t" the he cost of each cup of tea.

We need to set up the following system of equations:

$\left \{ {{3c+4t=25.50} \atop {t=\frac{2}{3}c}} \right.$

Applying the Method of Substitution, we must substitute the second equation into the first one and then solve for "c":

$3c+4(\frac{2}{3}c}})=25.50\\\\3c+\frac{8}{3}c=25.50\\\\\frac{17}{3}c=25.50\\\\c=\frac{25.50*3}{17}\\\\c=4.5$

 Therefore: Each cup of hot chocolate cost $4.5

Answer 2

Answer:

The cost of one cup of hot chocolate is $4.50

Step-by-step explanation:

Let

x ----> the cost of one cup of hot chocolate

y ----> the cost of one cup of hot tea

we know that

3x+4y=25.50 ------> equation A

y=(2/3)x -----> equation B

Solve the system of equations by substitution

substitute equation B in equation A and solve for x

3x+4(2/3)x=25.50

3x+(8/3)x=25.50

(17/3)x=25.50

x=25.50*3/17

x=$4.50

therefore

The cost of one cup of hot chocolate is $4.50