The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 1 van and 6 buses with 372 students. High School B rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students.

How many students can a van carry? How many students can a bus carry?

Hunter needs to make trail mix with nuts and dried fruit. The nuts cost $4 per pound and the dried fruit costs $3.50 per pound. Hunter can spend a total of $22 and he needs to make six pounds of trail mix.

Let x = the amount of nuts.

Let y = the amount of dried fruit.

How many pounds of dried fruit can Hunter purchase?

Guest Jan 26, 2018

#1**+1 **

V=Van

B=Bus

Solve the following system:

{6 B + V = 372 | (equation 1)

12 B + 4 V = 780 | (equation 2)

Swap equation 1 with equation 2:

{4 V + 12 B = 780 | (equation 1)

V + 6 B = 372 | (equation 2)

Subtract 1/4 × (equation 1) from equation 2:

{4 V + 12 B = 780 | (equation 1)

0 V+3 B = 177 | (equation 2)

Divide equation 1 by 4:

{V + 3 B = 195 | (equation 1)

0 V+3 B = 177 | (equation 2)

Divide equation 2 by 3:

{V + 3 B = 195 | (equation 1)

0 V+B = 59 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{V+0 B = 18 | (equation 1)

0 V+B = 59 | (equation 2)

Collect results:

**V = 18 - Number of students in each Van**

**B = 59 - Number of students in each Bus.**

x + y = 6

4x + 3.50y = 22, solve for x, y

Solve the following system:

{x + y = 6

4 x + 3.5 y = 22

In the first equation, look to solve for y:

{x + y = 6

4 x + 3.5 y = 22

Subtract x from both sides:

{y = 6 - x

4 x + 3.5 y = 22

Substitute y = 6 - x into the second equation:

{y = 6 - x

3.5 (6 - x) + 4 x = 22

3.5 (6 - x) + 4 x = 4 x + (21. - 3.5 x) = 0.5 x + 21.:

{y = 6 - x

0.5 x + 21. = 22

In the second equation, look to solve for x:

{y = 6 - x

0.5 x + 21. = 22

0.5 x + 21. = x/2 + 21:

x/2 + 21 = 22

Subtract 21 from both sides:

{y = 6 - x

x/2 = 1

**x = 2 - Pounds of nuts**

**y = 4 - Pounds of dried fruit**

Guest Jan 26, 2018

edited by
Guest
Jan 26, 2018