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Lyle, Katrina, and Mari have a combined age of 66 years. Their ages are three consecutive, even numbers. Let x represent the age of Lyle.

Write an equation that can be used to determine the age, x, of Lyle.

( )( ) + ( )= ( )

5 answers

To represent the ages of Lyle, Katrina, and Mari with \( x \) being Lyle's age, we can define their ages as follows:

  • Lyle's age: \( x \)
  • Katrina's age: \( x + 2 \) (the next even number)
  • Mari's age: \( x + 4 \) (the following even number after Katrina)

Since their combined age is 66 years, we can write the equation as:

\[ x + (x + 2) + (x + 4) = 66 \]

Now, we can simplify the equation:

\[ x + x + 2 + x + 4 = 66 \]

Combining like terms gives us:

\[ 3x + 6 = 66 \]

Therefore, the equation that can be used to determine the age, \( x \), of Lyle is:

\[ ( x ) + ( x + 2 ) + ( x + 4 ) = ( 66 ) \]

Andre hit 4 more home runs than twice the number of home runs Hassan hit. Together, they hit 10 home runs.

Write an equation which can be used to find the total number of home runs, h, Hassan hit.

(1 point)

( )( ) + ( )= ( )

Let \( h \) represent the number of home runs Hassan hit. According to the problem, Andre hit 4 more home runs than twice the number of home runs Hassan hit, which can be expressed as \( 2h + 4 \).

Since together they hit 10 home runs, we can set up the equation as follows:

\[ h + (2h + 4) = 10 \]

Now, we can represent this in the required format:

\[ ( h ) + ( 2h + 4 ) = ( 10 ) \]

This equation can be used to find the total number of home runs \( h \) that Hassan hit.

Amir bought a comic book for $9 and four pens. He spent a total of $25.(1 point)
Write an equation that can be used to find the cost of each pen, p.

( )p + ( ) = ( )

How much does each pen cost?

To represent Amir's total spending, we can set up the equation as follows:

  • The cost of each pen is \( p \).
  • Amir bought 4 pens, so the total cost for the pens is \( 4p \).
  • He also bought a comic book for $9.

The total amount spent is $25. Therefore, we can write the equation as:

\[ (4)p + (9) = (25) \]

To find the cost of each pen, we can solve the equation:

\[ 4p + 9 = 25 \]

Subtract 9 from both sides:

\[ 4p = 25 - 9 \] \[ 4p = 16 \]

Now, divide by 4:

\[ p = \frac{16}{4} \] \[ p = 4 \]

So, each pen costs $4.