Answer:
180 hamburgers
120 hotdogs
Step-by-step explanation:
In this question, we are asked to calculate the number of hamburgers and hotdogs sold by a company given the amount made by them and the total number of these snacks sold
We proceed as follows;
Let the amount of hotdogs sold be x and the amount of hamburgers sold be y.
We have a total of 300 snacks sold, mathematically;
x + y = 300 ..........(I)
Now let’s look at the prices.
x number of hotdogs sold at $2, this give a total of $2x hotdogs
y number of hamburgers sold at $3, this give a total of $3y.
Adding both to give total, we have ;
2x + 3y = 780.......(ii)
This means we have two equations to solve simultaneously. From equation 1, we can say x = 300 -y
Now let’s insert this in the second equation;
2(300-y) + 3y = 780
600-2y + 3y = 780
y = 780-600 = 180
Recall; x + y = 300
x = 300 -y
x = 300-180 = 120
Distribute the parentheses:
2(x + 1)
2 · x = 2x
2 · 1 = 2
2(x + 1) = 2x + 2
Answer:
x > 1/5
Step-by-step explanation:
All of these three triangle inequalities must be satisfied:
AB +BC > AC
BC +CA > BA
CA +AB > CB
___
Taking these one at a time, we have ...
AB +BC > AC
3x +4 + 2x +5 > 4x
x +9 > 0 . . . . . subtract 4x
x > -9
__
BC +CA > BA
2x +5 + 4x > 3x +4
3x > -1 . . . . . . subtract 3x+5
x > -1/3 . . . . . divide by 3
__
CA + AB > CB
4x + 3x +4 > 2x +5
5x > 1 . . . . . . subtract 2x+4
x > 1/5
___
The only values of x that satisfy all of these inequalities are those such that ...
x > 1/5
You can solve using the pythagorean theorem which is
a^2+b^2=c^2 where a and b are the legs and c is the hypotenuse in a right triangle.
12^2+x^2=24^2
144+x^2=576
x^2=432
x =20.78 (approximately)
