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# Set up a system of two equations to solve the following word problems?

Topic: Set up a system of two equations to solve the following word problems?
June 16, 2019 / By Bunny
Question: nacho has a collection of pens and key-chains. the number of pens is 5 more than twice the number of key chains . if the total amount of items in his collections is 62. how many of each does he have ??

## Best Answers: Set up a system of two equations to solve the following word problems?

Alline | 9 days ago
you need two variables to represent pens and key chains so lets use p and k then translate p = 5 + 2k number of pens(p) is(=) 5 more(+5) than twice the number of key chains(2k) p + k = 62 total number of means add em up now since we know what p = (5+2k) replace(substitute) the p in the other equation (5+2k)+k = 62 5+3k =62 3k = 57 k = 19 plug this in and find out what p is p = 5+2(19) p = 5+38 p = 43
👍 246 | 👎 9
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Originally Answered: System of Linear Equations - Word Problems?
1) You had the right idea, except I don't see how "75-cent" got turned into "\$0.45". Now substitute 90 for "x + y" in your first equation: (\$0.96 / 1 lb) = (\$0.75x + \$1.25y) / 90 lb Then start solving by multiply both sides by 90 lb: \$86.4 = \$0.75x + \$1.25y Substitute y = 90 - x into the last equation: \$86.4 = \$0.75x + \$1.25 (90 - x) Expand on the right: \$86.4 = \$0.75x + \$112.5 - \$1.25x Combine like terms: \$0.50x = \$26.10 x = 52.2 lbs 90 lbs - 52.2 lbs = 37.8 lbs = y 2) Let x be the amount (in gallons) of 15% to be used. Then 50-x is the amount of 25% to be used. 0.15x + 0.25(50-x) = 0.22 (50) Expand on both sides: 0.15x + 12.5 - 0.25x = 11 Combine like terms: 0.10x = 1.5 Divide by 0.10: x = 15 gallons of 15% 50-x = 35 gallons of 25% 3) (11+x) / (12+x) = 2/3 Cross multiply: 3 (11+x) = 2 (12+x) Expand: 33 + 3x = 24 + 2x Combine like terms: x = - 9

Uzal
P = Pens K = Key Chains T= Total (Pens + Key Chains) *P=2K + 5* T=P + K T=(2K + 5) + K *T= 3K + 5* 62 = 3K + 5 57 = 3K *19 = K* P= 2K + 5 P= 2(19) + 5 P= 38 + 5 *P=43* Pens = 43 Key Chains = 19
👍 100 | 👎 2

Rodney
p=pens k=key chains 1.62=p+k 2. p=2k+5 solve: 62=2k+5+k 62=3k+5 57=3k k=19 plug K into second equation equation and solve for p p=2(19)+5 p=43 or 62=p-19 p=43
👍 92 | 👎 -5

Mike
Try writing your answer in terms of 'n' For example, key chains = n pens = 2n + 5 total = 62 Trial and error helps here.
👍 84 | 👎 -12

Originally Answered: help in word problems in math involving system of linear equations?
car A has speed v (km/h) car B has speed w (km/h) distance = speed * time Distance travelled by the car till they meet is 140km v(48/60) + w(48/60) = 140 which simplifies to v + w = 175. For one of the car to catch up when travelling in the same direction means either v > w or w > v. For the question it doesn't matter which. If car A catches up with car B then v > w The distance needed to travel would be 140 + 4w = 4v or v - w = 35. The simultaneous equations are: v + w = 175. v - w = 35. Add them to eliminate w: 2v = 210 v = 105 km/h 105-35 = w = 70 km/h

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