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Paha777 [63]
3 years ago
11

If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in

the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number?
A.250,250
B.315,185
C.370,230
D.410,90
E.480,20
Mathematics
2 answers:
MariettaO [177]3 years ago
8 0
Let x be the first digit (ten's place) of the original number.
Let y be the second digit (one's place) of the original number.

(x + y)7 = original number
(x + y)7 = 10x + y
7x + 7y = 10x + y
6y = 3x

10y + x = (x + y) + 18
9y = 18
y = 2

6y = 3x
6(2) = 3x
12 = 3x
x = 4

x is the first digit, and y is the second digit, so the original number is 42.
kolbaska11 [484]3 years ago
3 0
The answer is A. 42

Solution:
Let x= ones digit, y=tens digit

1st condition (original number) : 7(x+y)=10y + x
2nd condition (new number by reversing the digits): 18+x+y=10x+y

simplifying:
1st condition: 6x=3y
2nd condition: x=2
substituting x=2 to 6x=3y
<span>y=4</span>
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A stick 43 inches long is broken into two pieces, so that one piece is twice as long as the other. How long are the two pieces?
allsm [11]

Answer:

One piece is  \frac{43}{3} inches and another piece is \frac{86}{3} inches


Step-by-step explanation:

Let smaller piece length be s

Let larger piece length be  l


Since total of two pieces is 43, we can write:

s+l=43


Also, one piece is twice as long as the other (so longer piece is definitely twice as the short piece), we can write:

l=2s


<em>Substituting equation 2 into equation one, we can solve for s:</em>

s+l=43\\s+(2s)=43\\3s=43\\s=\frac{43}{3}

<em>Thus longer piece is:</em>

l=2s=2(\frac{43}{3})=\frac{86}{3}

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The mg of PO that the nurse should administer in each of the three doses given weekly is calculated as

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= 1.5 mg of PO

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Step-by-step explanation:

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