# grouping  17 results

4 consecutive integers such that the sum of the first 3 integers is equal to the 4th
4 consecutive integers such that the sum of the first 3 integers is equal to the 4th Let n be our first consecutive integer. [LIST=1] [*]n [*]n + 1 [*]n + 2 [*]n + 3 [/LIST] The sum of the first 3 integers is equal to the 4th: n + n + 1 + n + 2 = n + 3 Simplify by grouping like terms: (n + n + n) + (1 + 2) = n + 3 3n + 3 = n + 3 3n = n n = 0 n = 0 n + 1 = 1 n + 2 = 2 n + 3 = 3 Check our work: 0 + 1 +2 ? 3 3 = 3 Our final answer is [B](0, 1, 2, 3}[/B]

A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find th
A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each? Let the boy's age be b and his brother's age be c. We're given two equations: [LIST=1] [*]b = c + 10 [*]b + 4 = 2(c + 4) [/LIST] Substitute equation (1) into equation (2): (c + 10) + 4 = 2(c + 4) Simplify by multiplying the right side through and grouping like terms: c + 14 = 2c + 8 [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B14%3D2c%2B8&pl=Solve']Type this equation into our search engine[/URL] and we get: c = [B]6[/B] Now plug c = 6 into equation (1): b = 6 + 10 b = [B]16[/B]

Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age?
Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age? Let a be Alvin's age and e be Elga's age. We have the following equations: [LIST=1] [*]a = e - 12 [*]a + e = 60 [/LIST] Plugging in (1) to (2), we get: (e - 12) + e = 60 Grouping like terms: 2e - 12 = 60 Add 12 to each side: 2e = 72 Divide each side by 2 [B]e = 36[/B]

Factoring and Root Finding
Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
* Binomial Expansions
* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs

If 11 times a number is added to twice the number, the result is 104
If 11 times a number is added to twice the number, the result is 104 Let [I]the number[/I] be an arbitrary variable we call x. 11 times a number: 11x Twice the number (means we multiply x by 2): 2x The phrase [I]is added to[/I] means we add 2x to 11x: 11x + 2x Simplify by grouping like terms: (11 + 2)x = 13x The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104: 13x = 104 <-- This is our algebraic expression To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get: x = [B]8[/B]

If x represents the first, or the smaller, of two consecutive odd integers, express the sum of the
If x represents the first, or the smaller, of two consecutive odd integers, express the sum of the two integers in terms of x If x is the first of two consecutive odd integers, then we find the next consecutive odd integer by adding 2 to x: x + 2 The sum of the two consecutive odd integers is expressed by x + (x + 2) Simplify by grouping like terms, we get: [B]2x + 2[/B]

In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there i
In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class? We start by declaring variables for boys and girls: [LIST] [*]Let b be the number of boys [*]Let g be the number of girls [/LIST] We're given two equations: [LIST=1] [*]b = g + 5 [*]b + g = 13 [/LIST] Substitute equation (1) for b into equation (2): g + 5 + g = 13 Grouping like terms, we get: 2g + 5 = 13 Subtract 5 from each side: 2g + 5 - 5 = 13 - 5 Cancel the 5's on the left side and we get: 2g = 8 Divide each side of the equation by 2 to isolate g: 2g/2 = 8/2 Cancel the 2's on the left side and we get: g = 4 Substitute g = 4 into equation (1) to solve for b: b = 4 + 5 b = [B]9[/B]

larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number? Declare variables for the 2 numbers: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 4 [*]l + s = 40 [/LIST] To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l. Subtract 4 from each side in equation (1) l - 4 = s + 4 - 4 Cancel the 4's and we get: s = l - 4 Our given equations are now: [LIST=1] [*]s = l - 4 [*]l + s = 40 [/LIST] Substitute equation (1) into equation (2) for s: l + l - 4 = 40 Grouping like terms for l, we get: 2l - 4 = 40 Add 4 to each side: 2l - 4 + 4 = 40 + 4 Cancelling the 4's on the left side, we get 2l = 44 Divide each side of the equation by 2 to isolate l: 2l/2 = 44/2 Cancel the 2's on the left side and we get: l = [B]22[/B]

Number Bonds
Free Number Bonds Calculator - Adds or subtracts 2 numbers and using grouping by 10 or 100. Also called number bonds or addition facts. Multiplies two numbers using tape diagrams.

Regrouping
Free Regrouping Calculator - Subtracts two numbers using regrouping

Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have
Sam has x model planes. Anton has 8 more planes than Sam does. How many model planes Does Anton have? how many planes do they have together? Sam has x Anton has [B]x + 8[/B] since the word [I]more[/I] means we add The word [I]together[/I] means we add, so we have: Sam + Anton = x + x + 8 Grouping like terms, we have: Sam + Anton = [B]2x + 8[/B]

Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are t
Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated? First 5 letters of the alphabet are {A, B, C, D, E} The 4 letters can be chosen as possible: 5 * 5 * 5 * 5 The number are not repeatable, so the 4 numbers can be chosen as: 10 * 9 * 8 * 7 since we have one less choice with each pick Grouping letters and numbers together, we have the following serial number combinations: 5 * 5 * 5 * 5 * 10 * 9 * 8 * 7 = [B]3,150,000[/B]

sum of 3 consecutive odd integers equals 1 hundred 17
sum of 3 consecutive odd integers equals 1 hundred 17 The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers? 1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4 2) We increment by 2 for each number since we have [I]odd numbers[/I]. 3) We set this sum of consecutive [I]odd numbers[/I] equal to 117 n + (n + 2) + (n + 4) = 117 [SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE] (n + n + n) + 2 + 4 = 117 3n + 6 = 117 [SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE] 3n + 6 - 6 = 117 - 6 [SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE] 3n + [S]6[/S] - [S]6[/S] = 117 - 6 3n = 111 [SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE] 3n/3 = 111/3 [SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE] [S]3[/S]n/[S]3 [/S]= 111/3 n = 37 Call this n1, so we find our other 2 numbers n2 = n1 + 2 n2 = 37 + 2 n2 = 39 n3 = n2 + 2 n3 = 39 + 2 n3 = 41 [SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE] ([B]37, 39, 41[/B]) 37 ← 1st number, or the Smallest, Minimum, Least Value 39 ← 2nd number 41 ← 3rd or the Largest, Maximum, Highest Value

the difference between 7 times a number and 9 less than a number
the difference between 7 times a number and 9 less than a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 7 times a number means we multiply x by 7 7x 9 less than a number means we subtract 9 from x x - 9 The difference between the two expressions means we subtract (x - 9) from 7x 7x - (x - 9) Simplifying this, we have: 7x - x + 9 Grouping like terms, we get: [B]6x + 9[/B]

the sum of 3 consecutive natural numbers, the first of which is n
the sum of 3 consecutive natural numbers, the first of which is n We have: n + (n + 1) + (n + 2) Grouping like terms, we have: [B]3n + 3[/B]

The sum of 3, 7, and a number amounts to 16
The sum of 3, 7, and a number amounts to 16 Let the number be n. A sum means we add. We're given: 3 + 7 + n = 16 Grouping like terms, we get: n + 10 = 16 [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B10%3D16&pl=Solve']Typing this equation into our search engine[/URL], we get: n = [B]6 [/B]

The sum of two consecutive integers if n is the first integer.
The sum of two consecutive integers if n is the first integer. consecutive means immediately after, so we have: n n + 1 [U]The sum is written as:[/U] n + n + 1 [U]Grouping like terms, we have:[/U] (n + n) + 1 [B]2n + 1[/B]