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Ber [7]
3 years ago
6

A chemical company makes two brands of antifreeze. The first brand is 85% pure antifreeze, and the second brand is 90% pure anti

freeze. In order to obtain 50 gallons of a mixture that contains 50% pure antifreeze, how many gallons of EACH brand of antifreeze must be used?
Mathematics
1 answer:
AleksandrR [38]3 years ago
4 0

Answer:

Let +a+ = gallons of 55% antifreeze needed

Let +b+ = gallons of 95% antifreeze needed

-----------------------

(1) +a+%2B+b+=+160+

(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+

-----------------------------------

(2) +.55a+%2B+.95b+=+.85%2A160+

(2) +.55a+%2B+.95b+=+136+

(2) +55a+%2B+95b+=+13600+

(2) +11a+%2B+19b+=+2720+

----------------------------

Multiply both sides of (1) by +11+

and subtract (1) from (2)

(2) +11a+%2B+19b+=+2720+

(1) +-11a+-+11b+=+-1760+

---------------------------

 

+8b+=+960+

+b+=+120+

and

(1) +a+%2B+120+=+160+

(1) +a+=+40+

-------------------

40 gallons of 55% antifreeze are needed

120 gallons of 95% antifreeze are needed

--------------------------------------

check:

(2) +%28+.55a+%2B+.95b+%29+%2F+160+=+.85+

(2) +%28+.55%2A40+%2B+.95%2A120+%29+%2F+160+=+.85+

(2) +%28+22+%2B+114+%29+%2F+160+=+.85+

(2) +136+=+.85%2A160+

(2) +136+=+136+

OK

Step-by-step explanation:

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2 years ago
The combined area of a square and a rectangle is 225 square yards. the length of the rectangle is 8 times the width of the recta
snow_lady [41]

Answer:

The rectangle:  <u>L = 40 yards.   W = 5 yards</u>

The square: The length and width are both <u>5 yards</u>.

Step-by-step explanation:

<u>Let L and W be the length and width of the rectangle. </u>

<u>Let l and w be the length and width of the square.</u>

Area for each is:

Rectangle:  L*W

Square:       l*w

We are told that <u>L*W + l*w = 225 yards^2</u>

We are also told that

<u>L = 8W </u>

and that

<u>l = W</u>

Since the sides of a square are all equal, w is also W:  <u>w=W</u>

Summarizing and substituting:

L*W + l*w = 225 yards^2

(8W)*W + W*W = 225 yards^2

8W^2 + W^2 = 225 yards^2

9W^2  = 225 yards^2

W^2 = 25

W = 5 feet

---------------------

Therefore, since L = 8W <u>,</u> <u>L = 40 yards.   W = 5 yards</u> for the rectangle.

The square:  l=W, so <u>l = 5 yards, and thus w=5 yards</u>

--------------------------

Check:

Do a rectangle of 40' x 5' plus a square of 5' x 5' have a total combined area of 225 yards^2?

40yd x 5yd + 5yd x 5yd = 225 yards^2?

200 yd^2 + 25 yd^2 = 225 yards^2?

YES

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Answer:

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have a great day! :)

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a line segment that connects two points of a circle.

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I had to move the decimal 6 places.

So,

1^-6

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~kaikers

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