Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

John and Mary have some marbles. The total number of marbles with John and Mary is $75$ times the ratio of the number of marbles with John to that with Mary. If Mary has $30$ marbles, find the number of marbles with John. $\newline$ (A) $20$ $\newline$ (B) $30$ $\newline$ (C) $45$ $\newline$ (D) $50$

View step-by-step help

View step-by-step help

Find what percent one number is of another: word problems

Full solution

Q. John and Mary have some marbles. The total number of marbles with John and Mary is

75

times the ratio of the number of marbles with John to that with Mary. If Mary has

30

marbles, find the number of marbles with John.

\newline

(A)

20

\newline

(B)

30

\newline

(C)

45

\newline

(D)

50

Define Variables: Let's denote the number of marbles with John as $J$ and the number of marbles with Mary as $M$ . According to the problem, $M$ is given as $30$ . The total number of marbles is $75$ times the ratio of the number of marbles with John to that with Mary. This can be written as: $\newline$ Total number of marbles = $J + M = 75 \times (\frac{J}{M})$
Substitute Value: We know that $M = 30$ , so we can substitute this value into the equation: $\newline$ $J + 30 = 75 \times (\frac{J}{30})$
Multiply Equation: To solve for $J$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by $30$ : $30 \times (J + 30) = 30 \times 75 \times \left(\frac{J}{30}\right)$
Simplify Equation: Simplifying both sides of the equation, we get: $30J + 900 = 75J$
Isolate Variable: Now, we need to isolate $J$ on one side of the equation. We can do this by subtracting $30J$ from both sides: $\newline$ $30J + 900 - 30J = 75J - 30J$
Divide to Solve: This simplifies to: $900 = 45J$
Divide to Solve: This simplifies to: $\newline$ $900 = 45J$ To find $J$ , we divide both sides of the equation by $45$ : $\newline$ $\frac{900}{45} = \frac{45J}{45}$
Divide to Solve: This simplifies to: $\newline$ $900 = 45J$ To find $J$ , we divide both sides of the equation by $45$ : $\newline$ $\frac{900}{45} = \frac{45J}{45}$ Solving for $J$ , we get: $\newline$ $J = \frac{900}{45}$ $\newline$ $J = 20$

More problems from Find what percent one number is of another: word problems

Question

70\%

\$10?

\newline

\$

Posted 3 months ago

Question

90\%

40

Posted 3 months ago

Question

What is the percent of change from

12

21

\newline

\newline

75 \%

\newline

9\%

\newline

75\%

\newline

9\%

Posted 3 months ago

Question

17

a prime number or a composite number?

\newline

\newline

(A) prime number

\newline

(B) composite number

Posted 2 months ago

Question

28

is what percent of

50 ?

\newline

\%

Posted 4 months ago

Question

2 \%

50

Posted 4 months ago

Question

12

60 \%

of what number?

Posted 4 months ago

Question

24

75 \%

of what number?

Posted 4 months ago

Question

84 \%

300

Posted 3 months ago

Question

15

is what percent of

25 ?

\newline

\%

Posted 4 months ago