Mathematics, 30.12.2020 15:30 Meirna

Five years ago, Max was twice as old as Bert. A year from now, the sum of their ages would be 30. How old are they now? Show your solution.

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Answer from: amandapill

Bert is 11 years old and Max is 17 years old.

Step-by-step explanation:

System of Equations

To solve the system of equations, we use two variables x and y. Let's make:

x = current age of Max

y = current age of Bert

x - 5 = age of Max five years ago

y - 5 = age of Bert five years ago

x + 1 = age of Max one year from now

y + 1 = age of Bert one year from now

According to the conditions of the problem, five years ago, Max was twice as old as Bert, thus:

x - 5 = 2(y - 5) [1]

It's also known a year from now, the sum of their ages would be 30:

x + 1 + y + 1 = 30 [2]

Operating and simplifying [1]:

x - 5 = 2y - 10

x = 2y - 5 [3]

Operating and simplifying [2]:

x + y + 2 = 30

x + y = 28 [4]

Substituting [3] in [4]:

(2y - 5) + y = 28

Simplifying:

3y - 5 = 28

3y = 33

y = 33/3 = 11

y = 11

From [3]:

x = 2*11 - 5

x = 22 - 5 = 17

x = 17

Max is 17 years old and Bert is 11 years old

Answer from: Quest

step-by-step explanation:

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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Five years ago, Max was twice as old as Bert. A year from now, the sum of their ages would be 30. Ho...