Answer:
Price of each muffin = $1.25
Price of each granola bar = $1.6
Step-by-step explanation:
Group 1:
6 muffins, 12 granola bars
Total money paid = $26.70
Group 2:
8 muffins, 15 granola bars,
Total money paid = $34.00
To find:
Price of each item?
Solution:
Let the price of one muffin = $
Let the price of one granola bar = $
As per group 1, the equation can be written as:
As per group 2, the equation can be written as:
.... (2)
Let us use elimination method to solve for and .
Multiplying equation (1) with 8 and subtracting (2) from it:
Using equation (1):
Therefore, the answer is:
Price of each muffin = $1.6
Price of each granola bar = $1.25
Looks like the labeled angle is bisected, in which case we can apply the angle bisector theorem. For this triangle, it says
Solve for :
Then either 
or 
, but since is a length, it must be positive. So <em>x</em> = 2.
20L = 20,000mL. 20,000 / (22+3) people = 800mL/person
Answer: her call lasted for 26 minutes.
Step-by-step explanation:
Let x represent the number of minutes for which her call lasted.
Rachel purchased a prepaid phone card for $30. Long distance calls cost 6 cents a minute using this card. Converting 6 cents to dollars, it becomes 6/100 = $0.06
This means that the cost of x minutes of long distance call is
0.06 × x = $0.06x.
If the remaining credit on her card is $28.44, it means that
0.06x + 28.44 = 30
0.06x = 30 - 28.44
0.06x = 1.56
x = 1.56/0.06
x = 26
Answer:
45
Step-by-step explanation:
AEF is a similar triangle to ABC. that means it has the same angles, and the sides (and all other lines in the triangle) are scaled from the ABC length to the AEF length by the same factor f.
now, what is f ?
we know this from the relation of AC to FA.
FA = 12 mm
AC = 12 + 28 = 40 mm
so, going from AC to FA we multiply AC by f so that
AC × f = FA
40 × f = 12
f = 12/40 = 3/10
all other sides, heights, ... if ABC translate to their smaller counterparts in AEF by that multiplication with f (= 3/10).
the area of a triangle is
baseline × height / 2
aABC = 500
and because of the similarity we don't need to calculate the side and height in absolute numbers. we can use the relative sizes by referring to the original dimensions and the scaling factor f.
baseline small = baseline large × f
height small = height large × f
we know that
baseline large × height large / 2 = 500
baseline large × height large = 1000
aAEF = baseline small × height small / 2 =
= baseline large × f × height large × f / 2 =
= baseline large × height large × f² / 2 =
= 1000 × f² / 2 = 500 × f² = 500 ×(3/10)² =
= 500 × 9/100 = 5 × 9 = 45 mm²
