Let’s say we have x gallons of brand 1 antifreeze and y gallons of brand 2 antifreeze. We know we need a total of 140 gallons, so one equation to relate the variables would be x+y=140. We also know that our final mixture should have 60% antifreeze, so another equation would be the weighted average of the two brands: .55x+.80y140=.60. (The weighted average is basically multiplying each % (55 and 80) by the number of gallons you have (x and y
) and adding those together, and dividing that by the total number of gallons (140). This equals the % of the final mixture (60).)
Now we have a system of two equations that we can solve.
x+y=140
.55x+.80y140=.60
*rearrange first equation to solve for y
:
y=140−x
*substitute this value in for y
in the second equation:
.55x+.80(140−x)140=.60
*use algebra and solve for x
:
The algebra shouldn’t be too complex, and I’m hoping you’re asking this about the setup rather than the actual algebra, and I’m lazy, and I used a calculator to solve this, and this is probably a long run-on sentence, and I got x=112
.
*plug this in to first equation and solve for y
:
y=140−112=28
x=112,y=28
112 gallons of brand 1 antifreeze, 28 gallons of brand 2 antifreeze. That’s a whole lot of antifreeze.
thanx heyaaaaaa
Answer:
Coefficients:
3, -5
Constant:
2
Step-by-step explanation:
I'm going to rewrite it:
Coefficients:
3, -5
Constant:
2
Answer:
18,432 pi cubic ft
Step-by-step explanation:
This problem can be solved using formula to find circumference and volume of sphere
for any sphere with radius r
circumference of sphere is 2* pi * r
volume of sphere is found by using formula 4/3*(pi*r^2)
Given circumference of sphere is 48 pi ft
therefore
2* pi * r = 48 pi ft
r = 48 pi ft/ 2* pi = 24 ft
substituting the value of r is formula of volume of sphere we have
volume of sphere is = 4/3*(pi*24^3) = 18,432 pi cubic ft
Answer:
Number of rocks and fossils collected by you is <u>1 and 24</u> respectively
Number of rocks and fossils collected by your friend is <u>3 and 12 </u>respectively
Step-by-step explanation:
Let the number of Rocks you collect be x
Let the number of Fossils you collect be y
Then the total number pf objects you collected will be
x + y = 25
x = 25 - y------------------------------(1)
Your friend collects three times as many rocks and half as many fossils as you.
This can be written as
3x + y (1/2) = 15
3x + (y/2) = 15-------------------(2)
Substituting (1) in (2)
3(25 - y) + (y/2) = 15
75 - 3y + (y/2) = 15
Grouping the like terms we get,
75 - 15 = 3y = (y/2)
60 = ( 6y - y /2)
60 x 2 = 6y -y
120 = 5y
y = 120/5
y = 24
Substituting y value in equation(1) we get
x = 25 - 24
x= 1
y= 24
Friends collects 3 times rock
so collects 3x =3(1) = 3rocks
Also he collects half as many fossils
That is
y/2 = 24/2 = 12 fossils
<u><em>Hope this help you! :)</em></u>
14 students play a brass instrument :)
