Question

caden and his little sister, nina, went blackberry picking. caden helped nina get started until she had 42 berries. when caden started picking his own berries, he picked 11 berries per minute while nina continued to pick 5 berries per minute.
which equation can you use to find m, the number of minutes it took for caden to have as many berries as nina?
$42 + 5m = 11m$
$5m + 11 = 42m$
after how many minutes did caden have as many berries as nina?
simplify any fractions.
minutes

Explanation:

Step1: Analyze the problem

Nina has 42 berries and picks 5 berries per minute, so her total berries after \( m \) minutes is \( 42 + 5m \). Caden picks 11 berries per minute, so his total berries after \( m \) minutes is \( 11m \). We need to find when \( 11m = 42 + 5m \). Wait, but the given equations are \( 42 + 5m = 11m \) and \( 5m + 11 = 42m \). Wait, maybe I misread. Wait, the problem says "which equation can you use to find \( m \), the number of minutes it took for Caden to have as many berries as Nina?"

Wait, Nina's berries: she had 42, then picks 5 per minute, so \( 42 + 5m \). Caden's berries: he picks 11 per minute, so \( 11m \). So when they are equal, \( 11m = 42 + 5m \), which is the same as \( 42 + 5m = 11m \). So the first equation \( 42 + 5m = 11m \) is correct. Now, let's solve it.

Step2: Solve the equation \( 42 + 5m = 11m \)

Subtract \( 5m \) from both sides: \( 42 = 11m - 5m \)
Simplify: \( 42 = 6m \)
Divide both sides by 6: \( m = \frac{42}{6} = 7 \)

Wait, but the second part is "After how many minutes did Caden have as many berries as Nina?" So we solve the correct equation. Wait, the first equation is \( 42 + 5m = 11m \), which we solved to \( m = 7 \). Let's check:

Nina's berries: \( 42 + 5(7) = 42 + 35 = 77 \)
Caden's berries: \( 11(7) = 77 \). Correct.

So the equation to use is \( 42 + 5m = 11m \), and solving it gives \( m = 7 \).

Answer:

The equation is \( 42 + 5m = 11m \), and the number of minutes is \( \boxed{7} \)