Question

1. a total of 145 adults and students that are going on the washington d.c. trip. there were 83 more students than adults. how many adults are going on the trip? how many students?

x =
equation 1
substitution:
y =
equation 2

1. at elisas printing company llc there are two kinds of printing presses for a total of 14 printing presses. model a which can print 70 books per day and model b which can print 55 books per day, allowing them to print 905 books per day. how many of model a?…model b?

x =
equation 1
substitution:
y =
equation 2

1. vince is trying to incorporate more exercise into his busy schedule. he has several short exercise routines he can complete at home. last week, he worked out for a total of 22 minutes by doing 1 arm routine and 1 abdominal routine. this week, he has completed 3 arm routines and 2 abdominal routines and spent a total of 56 minutes exercising. how long does each routine last?

x =
equation 1
substitution:
y =
equation 2

Explanation:

Problem 9

Step1: Define variables

Let $x$ = number of adults, $y$ = number of students

Step2: Set total people equation

$x + y = 196$

Step3: Set student-adult difference equation

$y = x + 83$

Step4: Substitute $y$ into first equation

$x + (x + 83) = 196$

Step5: Solve for $x$

$2x + 83 = 196$
$2x = 196 - 83 = 113$
$x = \frac{113}{2} = 56.5$

Step6: Solve for $y$

$y = 56.5 + 83 = 139.5$

Step1: Define variables

Let $x$ = number of Model A presses, $y$ = number of Model B presses

Step2: Set total presses equation

$x + y = 14$

Step3: Set total books printed equation

$70x + 55y = 905$

Step4: Isolate $y$ from first equation

$y = 14 - x$

Step5: Substitute $y$ into second equation

$70x + 55(14 - x) = 905$

Step6: Simplify and solve for $x$

$70x + 770 - 55x = 905$
$15x = 905 - 770 = 135$
$x = \frac{135}{15} = 9$

Step7: Solve for $y$

$y = 14 - 9 = 5$

Step1: Define variables

Let $x$ = time (minutes) for arm routine, $y$ = time (minutes) for abdominal routine

Step2: Set first week's time equation

$x + y = 22$

Step3: Set second week's time equation

$3x + 2y = 56$

Step4: Isolate $x$ from first equation

$x = 22 - y$

Step5: Substitute $x$ into second equation

$3(22 - y) + 2y = 56$

Step6: Simplify and solve for $y$

$66 - 3y + 2y = 56$
$-y = 56 - 66 = -10$
$y = 10$

Step7: Solve for $x$

$x = 22 - 10 = 12$

Answer:

Number of adults: $56.5$, Number of students: $139.5$
(Note: This result is non-integer, which may indicate a typo in the problem's numbers, but follows the given values)

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Problem 10