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Dmitry_Shevchenko [17]
3 years ago
14

A month ago, the ratio of nurses to doctors on a hospital staff was 3:5. Since that time, two additional nurses joined the staff

, no
nurses left and the number of doctors remained the same. The ratio of nurses to doctors on the hospital staff is now 4:5. How
many nurses are now on the staff?

Plz answer, I’ll givebrainliest
Mathematics
1 answer:
bija089 [108]3 years ago
6 0

Answer:

8

Step-by-step explanation:

The ratio of nurses to docters a month ago was 3:5. Now, it's 4:5. You can tell that there aren't 4 nurses because 3 => 4 is only one nurse. If you duplicate both ratios (multiply both sides by 2), you get 6:10 (for a month ago) and 8:10 (now). This is correct because 6+2=8. Hope it helps!

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\bf \begin{array}{clclll}&#10;3^{1001}&\qquad &4^{1002}\\&#10;\uparrow &&\uparrow \\&#10;a&&b&#10;\end{array}\\\\&#10;-----------------------------\\\\&#10;(a+b)^2-(a-b)^2\implies (a^2+2ab+b^2)-(a^2-2ab+b^2)&#10;\\\\\\&#10;a^2+2ab+b^2-a^2+2ab-b^2\implies 2ab+2ab\implies 4ab&#10;\\\\\\&#10;now\qquad 4(3^{1001})(4^{1002})=k12^{1001}\qquad &#10;\begin{cases}&#10;12^{1001}\\&#10;(4\cdot 3)^{1001}\\&#10;4^{1001}\cdot 3^{1001}&#10;\end{cases}

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