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| *Vultures Knob>>>Bicycle Shop |
Could someone help me with these math problems please? |
I've worked 100 other problems but my mind is numb to these - any suggestions on working them out? Could you show me HOW to work them out instead of just giving the answers since I'd like to understand as I'm studying for a test. Thanks so much! 1) 3b/6 + 2b = 10 2) 5/8 of the vehicles in the parking lot are cars. The rest are vans and trucks. If there are 780 cars in the lot, how many total vehicles are in the lot? 3) A mountain bike costs $86 more than twice the cost of a street bike. If together they cost $518, what is the cost of the mountain bike? 4) Browser's Book Store sold 864 items last week. They sold twice as many magazines as paperback books, and five times as many paperback books as hardbound books. How many of each product was sold? 5) James is 3 times as old as her brother Marshall. If the difference in their ages is 6 years, what is the age of each? 1) 3b/6 + 2b= 10 1/2b+ 2b= 10 2 1/2b= 10 b= 10/ 2 1/2 b= 4 2) If 5/8 of the cars is 780 then 1/8 is 780/5= 156 If 1/8=156 the 8/8 is 156x8=1248 There are 1248 vehicles in the lot 3) If we say that the cost of the street bike is x We can say that x+2x+86= 518 3x+86= 518 3x= 518-86 3x= 432 x= 432/3 x= 144 If the street bike is $144 then the mountain bike costs 144x2+86= $374 4) If the number of paperback books is x Then the number of magazines is 2x and the number of hardbround books sold is 1/5x Then x+ 2x+ 1/5x= 864 Then 3 1/5x= 864 Then x= 864/ 3 1/5 Then x= 270 So he sold 270 paperback books and 540 magazines and 54 hardbound books 5) If the age of Marshall is x then James age is 3x so 3x-x=6 2x= 6 x= 3 Marshall= 3 James= 3x3= 9 I hope this helps 1) 15b = 60 b=4 2) (5/8)x =780 x = 780*8/5 =1248 3) x= street bike price x + 86 +2x = 518 3x = 432 x = 144 86 + 2x = mountain bike cost 86 + 288 = 374 4) x = hardbound 5x = paper backs 2(5x) = magazines x + 5x + 10 x = 864 16x = 864 x = 54 5x = 270 10x = 540 5) J = 3M J - M = 6 3M -M = 6 2M = 6 M = 3 J = 9 #1. Not clear whether you mean (3b/6) + 2b = 10 or 3b/(6 + 2b) = 10. If the former cancel 3 to give you b/2 + 2b = 10 then multiply by 2 to give you b + 4b = 20 so 5b = 20 ---> b = 4 If the latter then multiply both sides by (6 + 2b) to give you 3b = 10(6 + 2b). Multiply out to get 3b = 60 + 20b ---> -17b = 60 ---> b = -60/17. I suspect it's the former. I would think that such questions would be easier to guide you to an answer VERBALLY, so I suspect that you really do want 6the answer, but here goes anyway. (liar) ;-) 1) It is always easier to work with whole numbers so the first thing is to get rid of all the fractions. Then you have to figure out what "b" is so you add all the b's together to find out how many b's equals the other side, then you divide everything by the number of b's. the Method is: to multiply everything (3b/6, 2b and 10) by the denominator of the fraction part (in this case 6), then add all the b's together, then divide everything by the number of b's (i.e. the result of 6x3b/6 + 6x2b) so that b = something) 2) These are usually tricky but you have to look at things the same way for proper perspective: 5/8 = 780/v (where v = the total number of vehicles in the lot) Same as before, Multiply both sides by the denominator that you know (8 x 5/8 = v and 8 x 780/v ) then multiply both sides by the other denominator, which in this case is v) You should now see something like 5v = 8 x 780. multiply everything out..... Now divide both sides by 5 to get your answer. 3) the toughest part is how to express these as an algebraic expression that you probably already know how to answer. Let the cost of a mountain bike = m and the cost of a street bike = s you know that m is equal to 86 more than double a street bike price, and that together they cost 518. So m equals +86 (86 dollars more than) 2s (double the price of a street bike) SO: m = 2s +86 and together they cost 518 or, one m and one s = 518, or : m + s = 518 Now take one and replace it in the other (i.e. m = "2s+86", put this where the m is in the other one) "m" + s = 518 "2s + 86" + s = 518 3s + 86 = 518 (subtract the spare number from both sides) 3s = 518-86 = 432 now divide both sides by 3 so that you can figure out what s is equal to. Now replace the s with this value in either equation to figure out how much a mountain bike costs. 4) Same idea but more unknown parts. The hardest part is putting it into an equation that looks like the others. Lets call the number of each item sold is the first letter of the item: magazines - m, hardcover = h and paperpacks is = p Five times as many paperbacks as hardcovers means that 5 times as many h's is equal to p or 5h = p you can replace the p with 5h in any other equation where there is a 'p'. Twice as many magazines as paperbacks means two times the p = m or m = 2p. and you know that the total items sold is 864; .... or m + p + h = 864. Replace the m with the item above that says what m equals and multiply and add it all out so that you have a number of h's and p's. Replace the p's with the thing above that says what p equals then you should be left with a bunch of one letter that equals a known (real) number, add all the amount of that one letter together to find out how many you have and then divide both sides of your equation by that number and you should know how many Now divide both sides by the certain number to find out.... I found out how many h's were sold. m + p + h = 864 (2p) + p + h = 864 3p + h = 864 but remember p = 5h 3x(5h) + h = 864 15h + h = 864 16h = 864 Now divide by 16 on both sides to figure out h and start replacing the h in the other equations to figure the other amounts out. 5) The hardest part is figuring out how to make the equations. I am more curious who names their daughter with a masculine name like James. James is 3 x Marshall's age j = 3m The difference in their ages is 6 years (ok you know James is older so you have to say James' age minus Marshall's age is 6 years): j - m = 6 Again replace the one with the other j - m = 6 but j = 3m, so 3m - m = 6 2m = 6 I will let you work it through from here. I hope that I did not give away too much. |
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