Answer:
Five touchdowns were made in the game
Step-by-step explanation:
Here, we want to know the number of touchdowns made during the game.
We proceed as follows;
Let the number of touch downs be x
So the total points earned through touchdowns is 6 * x = 6x
The number of scores is 10 times
Let the number of extra kick be y which means that the number of conversions will be (y-1)
So the total number of score times will be ;
x + y + y-1 = 10
x + 2y = 11 •••••••••(i)
Now let’s work with points
Touch down points = 6 * x = 6x
Points from extra kick = 1 * y = y
Points from 2-point conversions = 2(y-1) = 2y - 2
So;
6x + y + 2y -2 = 37
6x + 3y = 37 + 2
6x + 3y = 39
divide through by 3
2x + y = 13 •••••••(ii)
So now solve simultaneously
From ii, y = 13 - 2x
Put this into i
x + 2(13-2x) = 11
x + 26 - 4x = 11
x -4x = 11-26
-3x = -15
x = -15/-3
x = 5
There are five touchdowns in the game
Answer:
9...................................
Answers:
24 quarters
22 nickels
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Work Shown:
q = number of quarters
n = number of nickels
q+n = 46 coins total which solves to n = 46-q
25q = value of all the quarters in cents
5n = value of all the nickels in cents
25q+5n = value (cents) of all the coins of both types
25q+5n = 710 cents total = $7.10
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Apply substitution.
25q+5n = 710
25q+5(46-q) = 710
25q+230-5q = 710
20q+230 = 710
20q = 710-230
20q = 480
q = 480/20
q = 24
They have 24 quarters
This yields 25*q = 25*24 = 600 cents = $6.00 so far.
Use that value of q to find n
n = 46-q
n = 46-24
n = 22
They also have 22 nickels.
They have an additional 5n = 5*22 = 110 cents = $1.10
In total, they have 6.00+1.10 = 7.10 dollars which confirms we have the correct coin counts. Also, q+n = 24+22 = 46.
Answer:
TX
Step-by-step explanation:
