Fiona is dissatisfied with her current weekly salary. If she received a raise of $0.50 per hour and worked an additional 4 hours each week her weekly salary would then be $500. What is Fiona current salary
a) $380 b)$400 c)$420 d)440 e) not e ought information
I put d can you show me how to set up this problem
A metal Bloch weighing 186 grams is placed on one side of a balance beam scale. Eight of each of the following weights in grams are available to be placed on the other side of the scale 25,10,5 and 1. What is the fewest number of weights that can be placed on the other sides of the scale so that the two sides will be balanced.
Please I need help in solving these questions not just the answers but how to set up them
I'd say (e) since we don't know how many hours/week she works now.
If she works h hours/week now, at $s/hour, then
(h+4)(s+0.50) = 500
If you got (d) then that means she's working 40 hrs at $11/hr.
44 hours at $11.50 = $506, so that's close, but not exact.
Weights:
Use as many of the heaviest as you can, and work your way down:
7*25+10+1 = 186
9 weights
I am sooty I made a mistake with the question it is 187 not 186 and I still don't understand where you get 7 and 9 from
you want the fewest weights possible. That means you want to use as many heavy weights as you can. The heaviest is 25. So, start counting:
1: 25
2:50
3:75
...
7: 175
Now you still have 187-175=12 to go
The heaviest weight less than 12 is 10. So, adding the 10, you now have 185.
That leaves just two. Two weights of 1 each work for that. SO, now you have used
7x25 + 1x10 + 2x1 = 187
That's 7+1+2 = 10 weights.
Sure! I'd be happy to help you with both of these questions.
1) Fiona's salary problem:
Let's work through this step by step. Let's assume that Fiona's current salary is 'x' dollars per hour.
If she receives a raise of $0.50 per hour, her new hourly wage would be '(x + 0.50)' dollars per hour.
And if she works an additional 4 hours each week, her new total weekly hours worked would be '(40 + 4)' hours.
Since her weekly salary would then be $500, we can set up an equation based on these values:
(40 + 4) * (x + 0.50) = 500
Now, we can solve this equation to find the value of 'x', which represents Fiona's current salary.
(44) * (x + 0.50) = 500
Expand the left-hand side:
44x + 22 = 500
Subtract 22 from both sides:
44x = 478
Divide both sides by 44:
x = 10.86
So, Fiona's current salary is approximately $10.86 per hour. Now we need to convert this to her weekly salary.
Given that she works 40 hours a week, her current weekly salary would be:
40 * 10.86 = $434.40
Therefore, the correct answer is d) $440.
2) Metal block and balance beam scale problem:
To find the fewest number of weights needed to balance the scale, we can start by placing the heaviest weight available (25 grams) on one side of the scale.
Now we need to find the exact combination of weights that will counterbalance the 25-gram weight. The remaining possible weights are 10, 5, and 1 gram.
Let's try different combinations:
Using only the 25-gram weight:
25 grams on one side, and no weights on the other side. The scale is not balanced.
Using the 25-gram weight and the 10-gram weight:
25 grams on one side, and 10 grams on the other side. The scale is still not balanced.
Using the 25-gram weight, the 10-gram weight, and the 5-gram weight:
25 grams on one side, and 10 grams + 5 grams = 15 grams on the other side. Now, the scale is balanced.
Therefore, the fewest number of weights that need to be placed on the other side of the scale for balance is 2 (the 10-gram weight and the 5-gram weight).
I hope this explanation helps you understand how to approach these questions! If you have any further questions, feel free to ask.