Harrison went out to buy coffee for his classmates. There are 23 students in his class, counting Harrison himself. Some wanted mochas, and some wanted lattes. At the coffee shop nearby, a mocha costs $4.30, while a latte costs $3.50. If Harrison bought one coffee for each student — including one for himself — and spent $87.70, how many of each coffee did he buy?

Step-by-step explanation:

Let's represent the number of mochas bought with the variable , and the number of lattes bought with the variable .

Since there are students, the total number of mochas and lattes bought must be . This can be represented with the following equation:

We can also set up another equation based on the total amount spent on the coffe:

If we rearrange the first equation, we can solve for :

If we substitute this into the second equation, we can solve for :

Subtituting this back into the original equation, we can solve for :

Therefore, 9 mochas and 14 lattes were bought.

4.30 + 3.50 =7.80 x 7 = 54.60  7 of each

87.70 -54.60 = 33.10

33.10 = 7 x 3.50 = 24.50 = 7 more latte

$8.60 left over = 2 more mocha

=14 latte and 9 mocha

Step-by-step explanation:

answer: it's d

step-by-step explanation:

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!