Question

which expression represents the amount of money lisa earns this week? 6d + 4d + 8p + 146 + 7p; 6d + 4d + 8p + 7p; 6d + 4d + 8d + 146 + 7d; 6d + 4d + 8p + 146p + 7p

Explanation:

To solve this, we need to combine like terms. Like terms are terms with the same variable (or constant terms). Let's assume \( d \) and \( p \) represent different types of earnings (e.g., from different jobs or tasks).

Step 1: Identify like terms for \( d \) and \( p \)

• For terms with \( d \): We look at coefficients of \( d \).
• For terms with \( p \): We look at coefficients of \( p \).
• Constant terms (if any) are also like terms, but here we have \( 146 \) (a constant) and terms with \( d \) or \( p \).

Step 2: Analyze each option (by combining like terms)

Let’s assume the original earnings (before combining) have:

• Terms with \( d \): \( 6d, 4d, \) (maybe others)
• Terms with \( p \): \( 8p, 7p, \) (maybe others)
• Constant term: \( 146 \)

Option 1: \( 6d + 4d + 8p + 146 + 7p \)

• Combine \( d \)-terms: \( 6d + 4d = 10d \) (but wait, maybe there are more \( d \)-terms? Wait, no—wait, maybe the problem is about combining like terms. Wait, let's re-express:

Wait, maybe the original problem (not fully shown) has:

• \( d \)-terms: \( 6d, 4d, \) (and maybe \( 8d \) or \( 7d \)? No, let's check the options. Wait, the first option is \( 6d + 4d + 8p + 146 + 7p \). Let's combine like terms:

• \( d \)-terms: \( 6d + 4d = 10d \) (but if there are no other \( d \)-terms, this is correct for \( d \)-terms).
• \( p \)-terms: \( 8p + 7p = 15p \) (wait, no—wait, maybe the original has \( 8p \) and \( 7p \), so \( 8p + 7p = 15p \), and \( 6d + 4d = 10d \), plus \( 146 \). But let's check the other options:

Option 2: \( 6d + 4d + 8d + 146 + 7d \)

• \( d \)-terms: \( 6d + 4d + 8d + 7d = (6+4+8+7)d = 25d \), and no \( p \)-terms. But the problem mentions \( p \) (since other options have \( p \)), so this is wrong (no \( p \)-terms).

Option 3: \( 6d + 4d + 8p + 7p \)

• No constant term (\( 146 \) is missing), so this is wrong.

Option 4: \( 6d + 4d + 8p + 146p + 7p \)

• \( p \)-terms: \( 8p + 146p + 7p = 161p \), which is unlikely (too large).

Wait, maybe the correct approach is to combine like terms:

• Terms with \( d \): \( 6d + 4d \) (sum to \( 10d \), but if there are no other \( d \)-terms)
• Terms with \( p \): \( 8p + 7p \) (sum to \( 15p \))
• Constant term: \( 146 \)

Thus, the expression \( 6d + 4d + 8p + 146 + 7p \) combines \( d \)-terms, \( p \)-terms, and the constant. Let's verify:

• \( 6d + 4d = 10d \) (like terms for \( d \))
• \( 8p + 7p = 15p \) (like terms for \( p \))
• Constant: \( 146 \)

So the expression \( 6d + 4d + 8p + 146 + 7p \) (first option) is correct because it combines all like terms: \( d \)-terms, \( p \)-terms, and the constant \( 146 \).

Answer:

The expression \( 6d + 4d + 8p + 146 + 7p \) (first option) represents Lisa’s earnings by combining like terms for \( d \) and \( p \), and including the constant \( 146 \).