Question
$7.50 word problems
- From Mathematics: Algebra
- Closed, but you can still post tutorials
- Due on Oct. 28, 2007
- Asked on Oct 21, 2007 at 3:28:43PM
Q:
Please detail each step. Thanks
1. A shipment contains x film cartridges for 15 exposures each and x + 10 cartridges for 25 exposures each. What is the total number of photographs that can be taken with the film from this shipment?
2. Each of two stores has 2n+ 1 mouse pads costing $3 each and n-2 pads costing $2 each. How much more is the total value of the $3 mouse pads than the $2 mouse pads in the two stores.
3. A person 1.8 m tall is photographed with a 35-mm camera, and the film image is 20mm. Under the same conditions, how tall is a person whose film image is 16mm?
4. In testing the rate at which a polluted stream flows, a boat travels at 5.5 mi/h in still water took 5.0 h to go downstream between points, and it took 8.0 h to go upstream between the same two points. What is the rate of flow of the stream.
5. An air sample contains 4.0 ppm(parts per million) of two pollutants. The concentration of one is four times the other. What are the concentrations.
6. a 5.0 piece of tubing weighs 1.7lb. What is the weight of a 27-ft piece of the same tubing.
7. A ship enters the red sea from the suez canal, moving south 17.4 mi/h. Two hours later, a second ship enters the Red Sea and the southern end, moving north at 21.8 mi/h. If the red sea is 1390 long. When will the ships pass?
8. Fifty pounds of cement sand mixture is 40% sand. How many pounds of sand must be added for the resulting mixture to be 60% sand?
9. a karat equals 1/24 part of gold in an alloy(for ex. a 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200g of 14-karat gold?
10. An alloy weighing 20lb is 30% copper. How many pounds of another alloy, which is 80% copper must be added for the final alloy to be 60% copper?
1. A shipment contains x film cartridges for 15 exposures each and x + 10 cartridges for 25 exposures each. What is the total number of photographs that can be taken with the film from this shipment?
2. Each of two stores has 2n+ 1 mouse pads costing $3 each and n-2 pads costing $2 each. How much more is the total value of the $3 mouse pads than the $2 mouse pads in the two stores.
3. A person 1.8 m tall is photographed with a 35-mm camera, and the film image is 20mm. Under the same conditions, how tall is a person whose film image is 16mm?
4. In testing the rate at which a polluted stream flows, a boat travels at 5.5 mi/h in still water took 5.0 h to go downstream between points, and it took 8.0 h to go upstream between the same two points. What is the rate of flow of the stream.
5. An air sample contains 4.0 ppm(parts per million) of two pollutants. The concentration of one is four times the other. What are the concentrations.
6. a 5.0 piece of tubing weighs 1.7lb. What is the weight of a 27-ft piece of the same tubing.
7. A ship enters the red sea from the suez canal, moving south 17.4 mi/h. Two hours later, a second ship enters the Red Sea and the southern end, moving north at 21.8 mi/h. If the red sea is 1390 long. When will the ships pass?
8. Fifty pounds of cement sand mixture is 40% sand. How many pounds of sand must be added for the resulting mixture to be 60% sand?
9. a karat equals 1/24 part of gold in an alloy(for ex. a 9-karat gold is 9/24 gold). How many grams of 9-karat gold must be mixed with 18-karat gold to get 200g of 14-karat gold?
10. An alloy weighing 20lb is 30% copper. How many pounds of another alloy, which is 80% copper must be added for the final alloy to be 60% copper?
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full solutions with step by step explanations
- This tutorial hasn't been purchased yet.
- Posted on Oct 21, 2007 at 8:34:06PM
A:
Preview: ... * t<br><br>t = 1355.2/39.2 = 34.57 hours<br><br>You should check why this is true. If you replace this value for t in the first equation, d = 21.8 * t, you will see that d equals 753.63 miles.<br><br>If you do this for the other boat, you will see that the distance it travels in 34.57 hours equals 601.52 miles (d = 17.4 * t; 601.52 = 17.4 * 34.57). If you sum to that the distance travelled initially during those 2 hours, 34.8 miles, you get 636.32 miles. When you subtract this from the length of the Suez canal, which is 1390, you get 753.68 miles, which is approximately the distance travelled by the first boat, thus confirming our result. This problem was a bit tricky. I hope you managed to understand it.<br><br>8.<br><br>50 pounds is the total weight of the mixture and 40% of it is sand, so the total weight of sand in the mixture is 50 * 0.4 = 20 pounds. Now, we need the fraction of sand to be 60% of the total mixture, so we can write the equation:<br><br>(20 + x) / (50 + x) = 0.6<br><br>The numerator represents the weight of sand in the mixture, x being the amount added after, and the denominator, the total weight of the mixture, being x the extra weight of sand added. We rearrange the equation:<br><br>20 + x = 0.6* (50 + x)<br><br>20 + x = 30 + 0.6x<br><br>x - 0.6x = 30 - 20 <br><br>0.4x = 10<br><br>x = 25<br><br>This means we need to add an extra 25 pounds of sand to the mixture. You can confirm this by doing 20 + 25 (this is sand) divided by 50 + 25 (total components). This equals 60%<br><br>9.<br><br>The formula of the karat is x = 24 * Mg/Mt, where x is the karat rating, Mg the mass of pure gold and Mt the total mass of the sample. So, 200g of 14-karat gold means that its total mass is 200g.<br><br>14 = 24 * Mg/200<br><br>Mg = 200*14/24 ...
The full tutorial is about 1623 words long .
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help with word problems with explanations, step by step
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- Posted on Oct 21, 2007 at 9:10:21PM
A:
Preview: ... her they have traveled 1390 miles. See the file ship_pic.pdf for an illustration of why this is true.<br><br>So we know that the total distance traveled is the sum of the distances traveled by each ship:<br><br> 34.8 mi + 17.4 * T mi + 21.8 * T mi<br><br>Since this equals 1390 mi, we can solve for T<br><br> 34.8 mi + 17.4 * T mi + 21.8 * T mi = 1390 mi<br> (17.4 + 21.8) * T mi = 1390 - 34.8 mi<br> 39.2 * T mi = 1355.2 mi<br> T = 34.57 hours<br><br><br>8. Fifty pounds of cement sand mixture is 40% sand. How many pounds of sand must be added for the resulting mixture to be 60% sand?<br><br>The mixture is made up of sand and everything else. The fraction of sand is like this:<br><br> (fraction that is sand) = (weight of sand) / (total weight)<br><br>where (total weight) = (weight of sand) + (weight of everything else)<br><br>Since we know that the fraction that is sand is 0.4 (40%), and we know the total weight is 50lbs, then we can solve for the weight of the sand.<br><br> 0.4 = X / 50, X = 0.4 * 50 = 20 lbs.<br><br>So there is 20 lbs of sand, and 50 - 20 = 30 lbs of everything else.<br><br>If we add Y pounds of sand then the new fraction that is sand becomes<br><br> (20 + Y)/(20 + Y + 30)<br><br>Then if we want the (fraction of sand) to be 0.6, then we need this equation<br><br> 0.6 = (20 + Y)/(20 + Y + 30)<br><br>Now we can solve for Y<br><br> 0.6 = (20 + Y) / (50 + Y)<br>0.6 * (50 + Y) = 20 + Y<br>30 + 0.6 Y = 20 + Y<br>30 - 20 = Y - 0.6 Y<br>10 = 0.4 Y<br>10/0.4 = Y<br>Y = 25<br><br>So if we add 25 pounds of sand we'll have a total of 25 + 20 = 45 pounds of sand, and 30 pounds of everything else.<br><br>Then the fraction of sand is<br><br> 45 / (45 + 30) = 45 / 75 = 0.6<br><br>So we just need to add 25 pounds of sand<br><br><br>9. a karat equals 1/24 part of gold in an alloy(for ex. a 9-karat gold is 9/24 gold). How many grams o ...
Attachments:
ship_pic.pdf (13K)
The full tutorial is about 1862 words long plus attachments.
Attachments:
ship_pic.pdf (13K)