Questions: Matt has seven times as many stickers as David. How many stickers must Matt give David so that they will each have 120 stickers? Check that your answer is correct. Matt needs to give David stickers so that they both will have 120 stickers.

Solution Steps

To solve this problem, we need to set up an equation based on the given information. Let's denote the number of stickers David has as \( D \) and the number of stickers Matt has as \( M \). According to the problem, \( M = 7D \). We need to find the number of stickers \( x \) that Matt should give to David so that both end up with 120 stickers each. This can be set up as two equations:

1. \( M - x = 120 \)
2. \( D + x = 120 \)

We can solve these equations to find \( x \).

Let's define the variables:

• Let \( M \) be the number of stickers Matt has.
• Let \( D \) be the number of stickers David has.

According to the problem, Matt has seven times as many stickers as David: \[ M = 7D \]

We need to find out how many stickers Matt must give to David so that they both end up with 120 stickers each. Let \( x \) be the number of stickers Matt gives to David.

After giving \( x \) stickers:

• Matt will have \( M - x \) stickers.
• David will have \( D + x \) stickers.

We want both to have 120 stickers: \[ M - x = 120 \] \[ D + x = 120 \]

We know \( M = 7D \). Substitute \( M \) in the first equation: \[ 7D - x = 120 \]

We also know from the second equation: \[ D + x = 120 \]

Now we have two equations:

1. \( 7D - x = 120 \)
2. \( D + x = 120 \)

Add these two equations to eliminate \( x \): \[ (7D - x) + (D + x) = 120 + 120 \] \[ 8D = 240 \] \[ D = 30 \]

Now substitute \( D = 30 \) back into the second equation: \[ 30 + x = 120 \] \[ x = 120 - 30 \] \[ x = 90 \]

Let's verify the solution:

• Matt originally has \( M = 7D = 7 \times 30 = 210 \) stickers.
• David originally has \( D = 30 \) stickers.

After Matt gives 90 stickers to David:

• Matt will have \( 210 - 90 = 120 \) stickers.
• David will have \( 30 + 90 = 120 \) stickers.

Both will have 120 stickers, confirming our solution is correct.

Final Answer