Advertisements
Advertisements
Question
Solve for x: `(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (3x + 5)/(5x - 6)`.
Solution
Multiplying the Numerator and Denominator of R.H.S. by -x
`(3x^2 + 5x + 18)/(5x^2 + 6x + 12) = (-3x^2 + 5)/(-5x^2 - 6)`
Since, each ratio = `"Sum of antecedents"/"Sum of consequents"`
so `(3x^2 + 5x + 18 - 3x^2 - 5x)/(5x^2 + 6x + 12 - 5x^2 - 6x)`
= `(-3x^2 - 5x)/(-5x^2 - 6x)`
`(18)/(12) = (-3x^2 - 5x)/(-5x^2 - 6x)`
⇒ `(3)/(2) = (-3x^2 - 5x)/(-5x^2 - 6x)`
⇒ `(3)/(2) = (3x + 5)/(5x + 6)`
⇒ 15x + 18 = +x + 10
⇒ 9x = -8
⇒ x = `(-8)/(9).`
APPEARS IN
RELATED QUESTIONS
Convert the following ratio to a percentage.
3 : 4
Find the ratio of the following in the simplest fcrm:
5.60 and 2.40
If (p - x) : (q - x) be the duplicate ratio of p : q then show that: `1/"p" + 1/"q" = 1/"x"`
Reema has 24 notebooks and 18 books. Find the ratio of notebooks to books.
Find the sub-duplicate ratio of 9a2 : 49b2
If x : a = y : b, prove that `(x^4 + a^4)/(x^3 + a^3) + (y^4 + b^4)/(y^3 + b^3) = ((x + y)^4 + (a + b)^4)/((x+ y)^3 + (a + b)^3`
The ratio 5:4 is different from the ratio 4:5.
Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of the cost of a pen to the cost of a ball pen.
225% is equal to ______.
A doctor reports blood pressure in millimeters of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats, and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.
| Blood Pressure Ranges | |||
| Normal | Prehypertension | Hypertension (Very High) |
|
| Systolic | Under 120 mm Hg | 120-139 mm Hg | 140 mm Hg and above |
| Diastolic | Under 80 mm Hg | 80-89 mm Hg | 90 mm Hg and above |
Manohar is a healthy 37 years old man whose blood pressure is in the normal category.
- Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.
- If Manohar’s systolic blood pressure is 102 mm Hg, use the ratio from part (a) to predict his diastolic blood pressure.
- Calculate the ratio of average systolic to average diastolic blood pressure in the prehypertension category.
