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8090 [49]
3 years ago
14

Divide $500 in these ratios using the unitary method. A. 2:3 B. 3:7 C. 1:1

Mathematics
1 answer:
zysi [14]3 years ago
3 0

Answer:

A) 200 is to 300 dollars

B)150 is to 350 dollars

C) 250 is to 250

Step-by-step explanation:

Part A) We want to divide $500 in the ratio 2:3 using the unitary method.

The total ratio is 2+3=5.

This means one unit is \frac{500}{5}=$100

Therefore $500 in the ratio 2:3 is 2*100=200 to 3*100=300

Part B) We want to divide $500 in the ratio 3:7 using the unitary method.

The total ratio is 3+7=10.

This means one unit is \frac{500}{10}=$50

Therefore $500 in the ratio 3:7 is 3*50=150 to 7*50=350

Part C) We want to divide $500 in the ratio 1:1 using the unitary method.

The total ratio is 1+1=2.

This means one unit is \frac{500}{2}=$250

Therefore $500 in the ratio 1:1 is 1*250=250 to 1*250=250

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3 years ago
A train leaves Philadelphia at 2:00 PM. A second train leaves the same city in the same direction at 4:00 PM. The second train t
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Answer: First train speed shall be 42 mi/hr

Second train speed shall be 84 mi/hr

Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.

Step-by-step explanation:

What is the 1st train's head start in miles?

Let +s+ = the speed of the 1st train in mi/hr

From 2PM to 4PM is 2 hrs

+d%5B1%5D+=+s%2A2+

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

Let +d+ = distance the 2nd train travels until

it overtakes the 1st train

From 4PM to 6PM is 2 hrs

Start time when the 2nd train leaves

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

Equation for 1st train:

(1) +d+-+2s+=+s%2A2+

Equation for 2nd train:

(2) +d+=+%28+s%2B42+%29%2A2+

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

Substitute (2) into (1)

(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+

(1) +2s+%2B+84+-+2s+=+2s+

(1) +2s+=+84+

(1) +s+=+42+

and

+s%2B+42+=+42+%2B+42+

+s+%2B+42+=+84+

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

The 1st train's speed is 42 mi/hr

The 2nd train's speed is 84 mi/hr

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

check:

(2) +d+=+%28+s%2B42+%29%2A2+

(2) +d+=84%2A2+

(2) +d+=+168+

and

(1) +d+-+2s+=+s%2A2+

(1) +d+-+2%2A42+=+42%2A2+

(1) +d+=+84+%2B+84+

(1) +d+=+168+

8 0
3 years ago
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