Answer:
p= 2.5
q= 7
Step-by-step explanation:
The lines should overlap to have infinite solutions, slopes should be same and y-intercepts should be same.
Equations in slope- intercept form:
- 6x-(2p-3)y-2q-3=0 ⇒ (2p-3)y= 6x -2q-3 ⇒ y= 6/(2p-3)x -(2q+3)/(2p-3)
- 12x-( 2p-1)y-5q+1=0 ⇒ (2p-1)y= 12x - 5q+1 ⇒ y=12/(2p-1)x - (5q-1)/(2p-1)
<u>Slopes equal:</u>
6/(2p-3)= 12/(2p-1)
6(2p-1)= 12(2p-3)
12p- 6= 24p - 36
12p= 30
p= 30/12
p= 2.5
<u>y-intercepts equal:</u>
(2q+3)/(2p-3)= (5q-1)/(2p-1)
(2q+3)/(2*2.5-3)= (5q-1)/(2*2.5-1)
(2q+3)/2= (5q-1)/4
4(2q+3)= 2(5q-1)
8q+12= 10q- 2
2q= 14
q= 7
Coffee = $12
Tea = $8
Total cost = $2600
Total Case = 250
Assumed all 250 cases are Tea
250 x 8 = 2000
Difference in amount
2600 - 2000 = 600 (so $600 was from the coffee)
Difference between the price of coffee and tea
12 - 8 = $4
Number of cases of coffee
600 ÷ 4 = 150
Number of cases of tea
250 - 150 = 100
150 cases of coffee were ordered
Answer:
120 pounds
Step-by-step explanation:
1. divide 45 by 15
45 / 15 = 3
2. Each box costs 3 pounds each
3. multiple 3 by 40.
4. 40 x 3 = 120
Answer:
Let's denote students in D = in the drama club , S = in a sports team
P(D) = 85/330
P(S) = 200/330
P(D and S) = 60/300
P(D or S) = P(D) + P(S) - P(D and S) = 85/330 + 200/330 - 60/330 = 15/22
P(neither D nor S) = 1- 15/22 = 7/22
Step-by-step explanation:
