Answer:
The Miami Dolphins had 3 touchdowns and 3 field goals.
Step-by-step explanation:
It is given that During their last game, the Miami Dolphins scored 6 times, for a total score of 30 points. They scored 7 points for each touchdown and 3 points for each field goal.
We need to write and solve the system of equations to find the total touchdowns and field goals scored.
Let x represents the number of touchdowns.
Let y be the number of field goals.
It is given that the Miami Dolphins scored 6 times
....(1)
They scored 7 points for each touchdown and 3 points for each field goal.
The total score is 30 points:
...(2)
Put the value of x from equation (1) into equation (2).
Put y = 3 in equation 1.
Hence, the Miami Dolphins had 3 touchdowns and 3 field goals.
Answer:
11 of 20p, 22 of 10p and 33 of 5p
Step-by-step explanation:
Eva has 20p, 10p and 5p coins, total of £6.05 = 605p
Let 20p=x, 10p=y, 5p=z
<u>Then</u>:
- 20x + 10y + 5z = 605
- y : x = 2 : 1 ⇒ x= y/2
- y : z = 2 : 3 ⇒ z= 3y/2
<u>Rewriting the first equation considering next two:</u>
- 10y + 10y + 7.5y = 605
- 27.5y = 605
- y= 605/27.5
- y= 22
- x= y/2 = 22/2 = 11
- z = 3y/2 = 3*11 = 33
<u>Answer:</u> 11 of 20p coins, 22 of 10p coins and 33 of 5p coins
This is a system of equations. You can solve it by substitution or elimination. I'm going to use substitution x - 2y = -4.5; add 2y to each side x - 2y + 2y = -4.5 + 2y; simplify x = 2y - 4.5 2(2y - 4.5) + 3y = 12 4y - 9 + 3y = 12 7y - 9 = 12 7y - 9 + 9 = 12 + 9 7y = 21 y = 3 <--------first answer x - 2y = -4.5 x - 2(3) = -4.5 x - 6 = -4.5 x -6 + 6 = -4.5 + 6 x = 1.5 <--------second answer Check: 2(1.5) + 3(3) = 12? 3 + 9 = 12? 12 = 12; It checks 1.5 - 2(3) = -4.5? 1.5 - 6 = -4.5? -4.5 = -4.5; It checks x = 1.5 and y = 3 <-----------Final Answer
