Find two numbers such that the second number is 3 more than twice the first number and the sum of the number is 72.?
You can do this by using simultaneous equations. We'll call the first number x and the second number y. As the second number (y) is 3 more than TWICE the first number (x), we can express this through the equation: y=2x+3 And as the sum of the two numbers (x+y) is 72, we can also use the equation: x+y=72 If we put these together, we are able to simplify these down using the method of simultaneous equations: y=2x+3 x+y=72 As we already know that y=2x+3, we can substitute the value of y into the second equation, giving us: x+(2x+3)=72 We can then simplify this to get: 3x+3=72 3x=72-3 3x=69 x=69/3 x=23 As we now have the value of x to be 23, we can substitute this back in to the first equation, y=2x+3 y=2(23)+3 y=46+3 y=49 Therefore the value of x is 23 and the value of y is 49.
The sum of two number is 30. twice the larger number is 3 less than 7 times the smaller number.?
first number lets call a. second, the bigger, is b. a + b = 30 2b= 7a -3 now solve by substitution. 2b= 7a -3 divide by two b= 7a/2 - 3/2 now plug this into the first equation. a + (7a/2 - 3/2) = 30 add 3/2 to both sides and combine the a terms. if you have to show your work continue from there. im just gonna guess and check for now. start by making a list of possibilities: 1, 29 2, 28 3, 27 4, 26 5, 25 6, 24 7, 23 8, 22 9, 21 10, 20 i found it. its 7 and 23. 7 + 23 = 30. 23 * 2 = 46 7 * 7= 49 so 46 is three less than 49. IT WORKS: 7 and 23!
Let the small unknown number = xX + 3X = 724X = 72X=72/4 = 18The small number is = 18.The larger number can be solved by how we defined it earlier.Let the bigger number = Y.Y=big numberRemember it's also equal to 3 times the small number.3X=YWe substitute the known value of X3 * 18 = Y = 54
Let 4X, 2X, X be the numbers.Then, average of reciprocals of these numbers ( 1/4X + 1/2X + 1/X ) ÷ 3 = 7/72 (given in the problem).That is, ( 1/4X + 2/4x + 4/4X ) ÷ 3 = 7/72.That is, ( 7/4X) ÷ 3 = 7/72. Or, 7/4X =( 7×3)/72. That is, 7/4X =21/72 Or, 7/4X =7/24.By equating the numerators and denominators of both sides, we have 7 = 7. And 4X = 24. Or, X = 6.So, the first number = 4X = 4×6 = 24Second number = 2X = 2×6 = 12Third number = X = 6.Checking for correctness :-Numbers: 24, 12,& 6.Average of sum of their reciprocals = {(1/24) + (1/12) +(1/6)} ÷ 3 ={(1/24) + (2/24) + (4/24)} ÷ 3= (7/24) ÷ 3 = 7/(24×3) = 7/72 = value mentioned in the problem question given.
let x be first and y be the second number4x - y = -21x + 4y = 334x + 16y = 1324x - y = -2116y - (-y) = 132 - (-21)17y = 153y = 153/17 = 9x + 4(9) = 33x + 36 = 33x = 33–36x = -3the first number is -3 and the second number is 9
Sum of 3 numbers is 66First number is a, second number is b and third number is ca+b+c=66first number is twice of the second number i.e a=2bthird number is one-third of the first c=(1/3)aa=2b, c=2b/3substitute above value in the a+b+c=662b+b+(2b/3)=663b+(2b/3)=66L.C.M is 3((9b+2b)/3)=6611b/3=6611b=66*3b=6*3=18a=2b=2*18=36c=a/3=36/3=12so a is 36, b is 18 and c is 12
Let the numbers be a,b and cATQa=2b……….(I)a=3c……….(ii)a+b+c=462 (avg is 154)a+(a/2)+(a/3)=462 ( from I and ii )11 a = 462 * 6a= 252So, b = 126 and c= 84Therefore, a-c= 252–84 =168.
(x + 2x + 3x)/3 = 49.5Multiply both sides by 3 to get rid of the fraction:x + 2x + 3x = 148.56x = 148.5Divide by 6:x = 24.75Prove this by substituting for x in the original equation:(24.75 + 2*24.75 + 3*24.75)/3 = 49.5do the multiplication first:(24.75 + 49.5 + 74.25)/3 = 49.5Now do the addition, and then the division:148.5/3 = 49.549.5 = 49.5
Let the first, second and third numbers are x, y and z respectively.According to the three conditions of the problem, three equations arises. They are:x + y + z = 10 ……….(I)y = x + z ……………..(II)y = z - 2 ………………(III)From equations (II) and (III), we getx + z = z - 2or, x = -2Putting equation (II) y = x + z in equation (I), we getx + (x + z) + z = 10or, 2(x+z) = 10or, x + z = 5or, -2 + z = 5 [since, x = -2]or, z = 7Finally, putting z = 7 in equation (III), we gety = 7 -2or, y = 5Hence, the answer is,First number (x) = -2Second number (y) = 5Third number (z) = 7Cheers!
It's a question of equation with two variables .Considering the two number as a & b . Two different conditions are been given to you in the form of words which need to be converted in the form of equations.So Condition 1 : 2a+3b =92Condition 2 : 4a-7b =2Since second condition have 4 as the coefficient of a , so will be trying making coefficient of a as 4 in first condition and for that we need to multiply the complete condition by 2.Which becomes2*(2a+3b=92)4a+6b=184OR4a= 184-6bSubstituting value of 4a in condition two ,184-6b-7b=213b=182b=14Substituting value of b in any condition will give you the value of a .2a+3(14)=922a+42=922a=50a=25b=14are the numbers.