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marissa [1.9K]
3 years ago
13

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total

of 5 people took the trip. She was able to purchase coach tickets for ​$380 and first class tickets for ​$1080. She used her total budget for airfare for the​ trip, which was ​$4000. How many first class tickets did she​ buy? How many coach tickets did she​ buy?
Mathematics
1 answer:
quester [9]3 years ago
5 0

Answer:

Sarah bought 2 coach tickets and 3 first class tickets.

Step-by-step explanation:

Let c and f represent the numbers of coach and first class tickets purchased.  Then c + f = 5, so that c = 5 - f.

The pricing equation is therefore

$380c + $1080f = $4000.  Subbing 5 - f for c, we get the revised equation

380(5 - f) + 1080f = 4000.

After simplification, this becomes:

-380f + 1080f = 2100, or

700f = 2100.

Then f = 3 and c = 5 - f = 5 - 3 = 2.

Sarah bought 2 coach tickets and 3 first class tickets.

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Two factory plants are making tv panels. Plant A produced 2000 fewer panels than Plan B did. Two percent of the panels from Plan
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Answer:

Plant A produced 15,000 panels.

Step-by-step explanation:

Let plant B produce x panels

Plant A then produced x - 2000 panels

2% of panels from plant A were defective

3% of panels from plant B were defective

The two plants together produced 810 defective panels so;

2/100(x - 2000) + 3/100(x) = 810

0.02x - 40 + 0.03x = 810

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3 years ago
ASAP HELP FOR NUMBER 13!!
horrorfan [7]
Problem 13a

Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.

Another point on this line is (3,8) which is drawn from the second column.

Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2

Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2

Plug those into y = mx+b and we get y = 2x+2

Answer: y = 2x+2

==============================================
Problem 13b

(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20

Another point on this line is (3,8) as drawn from the second column

Slope: 
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4

Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20

Answer: y = -4x+20

==============================================
Problem 13c

(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.

Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5

Note: the fraction 3/2 is equivalent to the decimal form 1.5

Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2

So we can now update y = mx+b to y = 1.5x+2

Answer: y = 1.5x+2

Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write y = \frac{3}{2}x+2
==============================================
Problem 13d

(0,20) is on the line. So the y intercept is 20, indicating that b = 20

(3,11) is also on the line

Again as done with 13a-13c, I'm only looking at the first two columns. 

Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3

Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier

Answer: y = -3x+20
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