Plug em into a calculator and they are both irrational
We can set up an equation to solve this problem, but first we need to write out what we know.
$20 overall
$0.24 every minute
$13.52 remaining on the card
Now that we know our information, we can set it up in an equation.
20 - 0.24x = 13.52
The 20 represents $20 overall when she first got the phone card.
We are then subtracting $20 from how must it costs a minute (which is 24 cents). The 'x' indicates the number we are trying to find (how many minutes her call lasted). Lastly, 13.52 is the result of everything, since she has $13.52 remaining on the card.
We can now solve the equation:
20 - 0.24x = 13.52
-0.24x = 13.52 - 20 /// subtract 20 from each side
-0.24x = -6.48 /// simplify
x = 27 /// divide each side by -0.24
Our solution is: x = 27.
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An easier way to solve this problem would be to first, subtract the total amount of money she had on the card when she first got it, and then the remaining total she ended up with.
$20 - $13.52 = $6.48
So, she spent a total of $6.48 on long distance calls, but since we are looking for how many minutes, we need to divide the total she spent and how much it costs per minute.
6.48 ÷ 24 = 27
We receive the same amount of minutes spent just like we did the last way we solved.
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Salma spent 27 minutes on the phone.
Option C: There are no solutions
Explanation:
The linear equations is graphed.
We need to determine the solution of the system of equations.
The solution of the equations can be determined by finding the point of intersection of the two equations.
From the figure, it is obvious that the two equations are parallel to each other.
Also, the parallel lines have the same slope and the parallel lines never intersect.
Hence, the system consisting of parallel lines have no solution.
Therefore, the solution to the system of linear equations graphed is no solution.
Thus, Option C is the correct answer.
Answer:
$4600
Step-by-step explanation:
Write an equation to represent the problem.
Interest is calculated by multiplying the interest rate with the investment. <u>Multiplying each of the rates</u> (2%, 7% and 9%) <u>in decimal form with the investment amount is equal to the annual interest</u>, (828).
Convert a percentage to decimal form by dividing by 100:
2% ÷ 100 => 0.02
7% ÷ 100 => 0.07
9% ÷ 100 => 0.09
let "P" represent the amount of money for the total investment
0.02P + 0.07P + 0.09P = 828
Use the equation to solve for "P". Simplify by collecting like terms (numbers that have the same variable) then isolate "P" by moving the other numbers to the right side. To move a number to the other side, do it's reverse operation to both sides of the equation. (The reverse of multiplying is dividing).
0.02P + 0.07P + 0.09P = 828 Collect like terms
0.18P = 828 Isolate "P"
0.18P/0.18 = 828/0.18 Divide both sides by 0.18
P = 828/0.18 "P" is isolated because 0.18 cancelled out. Simplify.
P = 4600 Total investment
Therefore the total investment is $4600.
Answer:
There are 585 adults and children
Step-by-step explanation:
Let the number of adults be a, number of children be c and the number of seniors be a
Amount made per group;
adults; 52 * a = 52a
Children : 26 * c = 26c
Seniors = 20 * s = 20s
Adding all will give 20,490
52a + 20s + 26c = 20 490 ••••(i)
Now let us work with the ratios;
a : s = 6 : 1
a/s = 6/1
a = 6s •••••(ii)
Lastly;
a/c = 4/9
4c = 9a ••••(ii)
We want to get a + c
From the first equation , let’s substitute
52(6s) + 20s + 26c = 20,490
26c = 6.5 (4c)
but 4c = 9a; 6.5(9a)
But a = 6s
So we have; 6.5(9)(6s) = 351s
so we have;
312s + 351s + 20s = 20,490
683s = 20,490
s = 20490/683
s = 30
Recall;
a = 6s = 6 * 30 = 180
4c = 9a
4c = 9 * 180
c = (9 * 180)/4 = 405
So the total number of children and adult is a + c
405 + 180 = 585
