To find the correct equation that represents the relationship between the number of 3 lb weights ([tex]\( x \)[/tex]) and the number of 10 lb weights ([tex]\( y \)[/tex]) adding up to a total of 50 pounds, we need to express this scenario mathematically.
Let's break it down step-by-step:
1. Representation of the weights:
- [tex]\( x \)[/tex] is the number of 3 lb weights.
- [tex]\( y \)[/tex] is the number of 10 lb weights.
2. Expression of the total weight:
- The weight contributed by the 3 lb weights is [tex]\( 3x \)[/tex].
- The weight contributed by the 10 lb weights is [tex]\( 10y \)[/tex].
3. Total weight equation:
- According to the problem, the sum of these weights is 50 lb. This can be written as:
[tex]\[
3x + 10y = 50
\][/tex]
Now, let's analyze the given equations to identify the correct one:
1. Option 1: [tex]\( 3x - 10y = 50 \)[/tex]:
- This equation suggests that the difference between the weights is 50 lb, which does not match the described scenario.
2. Option 2: [tex]\( 3x = 50 - 10y \)[/tex]:
- We can check if this equation is equivalent to [tex]\( 3x + 10y = 50 \)[/tex]. By adding [tex]\( 10y \)[/tex] to both sides of [tex]\( 3x = 50 - 10y \)[/tex]:
[tex]\[
3x + 10y = 50
\][/tex]
- This is indeed the rearrangement of the original correct equation [tex]\( 3x + 10y = 50 \)[/tex]. Hence, this is the correct equation.
3. Option 3: [tex]\( 50 + 10y = 3y \)[/tex]:
- This equation equates the sum of 50 and the weight contributed by 10 lb weights to the weight contributed by 3 lb weights, which does not make sense in this context.
4. Option 4: [tex]\( 50 + 3y = 10y \)[/tex]:
- This equation suggests that adding 50 lb to the weight of some 3 lb weights equals the weight of some 10 lb weights. This also does not fit the scenario described.
The correct equation that can be used to find the number of each type of weight Bob has is:
[tex]\[
3x = 50 - 10y
\][/tex]
