Solve the following problems according to the definition of ratio.

Lisa has 12 more stickers than John, and together they have 60 stickers. What is the ratio of the number of Lisa's stickers to the number of John's stickers?

1 answer

Let's denote the number of John's stickers as \( J \) and the number of Lisa's stickers as \( L \).

From the problem, we know two things:

  1. Lisa has 12 more stickers than John: \[ L = J + 12 \]

  2. Together, they have a total of 60 stickers: \[ L + J = 60 \]

Now we can substitute the expression for \( L \) from the first equation into the second equation:

\[ (J + 12) + J = 60 \]

This simplifies to:

\[ 2J + 12 = 60 \]

Next, we subtract 12 from both sides:

\[ 2J = 48 \]

Now, divide both sides by 2:

\[ J = 24 \]

Using the value of \( J \), we can find \( L \):

\[ L = J + 12 = 24 + 12 = 36 \]

Now we have:

  • John has 24 stickers.
  • Lisa has 36 stickers.

Next, we can find the ratio of the number of Lisa's stickers to the number of John's stickers:

\[ \text{Ratio of Lisa's stickers to John's stickers} = \frac{L}{J} = \frac{36}{24} \]

To simplify this ratio, we divide both the numerator and the denominator by their greatest common divisor, which is 12:

\[ \frac{36 \div 12}{24 \div 12} = \frac{3}{2} \]

Thus, the ratio of the number of Lisa's stickers to the number of John's stickers is:

\[ \boxed{\frac{3}{2}} \]