Solve each part with variables a) A certain number of matches are needed to fill

Question

Solve each part with variables a) A certain number of matches are needed to fill 24boxes, with each box containing the same number of matches.when 4less matches are put into each box , there are enough for 28boxes.Find the total number of matches. b) Mr. Kumar lives in the eastern part of singapore. he visitshis aged parents who lives 36 km away .every weekend . he findsthat if he increases the average speed of his vehcile by 12 km /hhe could save 9 minutes of his travelling time .Find the speed atwhich he travels before the increase in speed. Solve each part with variables a) A certain number of matches are needed to fill 24boxes, with each box containing the same number of matches.when 4less matches are put into each box , there are enough for 28boxes.Find the total number of matches. b) Mr. Kumar lives in the eastern part of singapore. he visitshis aged parents who lives 36 km away .every weekend . he findsthat if he increases the average speed of his vehcile by 12 km /hhe could save 9 minutes of his travelling time .Find the speed atwhich he travels before the increase in speed.

Explanation / Answer

Therefore, we can set these two expressions for the totalnumber of matches equal:
24x = 28(x-4). 24x = 28x - 112 112 = 4x 28 = x.
Plugging this value for x into one of our original expressionsfor the total number of matches, we see that there are 24*28 or 672matches.
b) Let's call the speed at which he travels before theincrease in speed 'r' and the amount of time it takes him at thisspeed 't'.
Then, using the formula: distance = rate*time, we have: 36 = r*t.
Then we are told that if he increases his rate by 12 km/hr hecould save 9 minutes. Thus, 36 = (r+12)(t-9).
Setting these two equal, we have: rt = (r+12)(t-0.15). *Note that 9 minutes is 0.15hours.
Expanding, we have:
rt = rt - 0.15r + 12t - 1.8.
Subtracting out the rt term and solving for t, we get: t = 0.0125r + 0.15.
Plugging this into our original equation 36 = rt, wehave: 36 = r(0.0125r+0.15).
Expanding, we see: 36 = 0.0125r2+0.15r.
Moving all the terms to the right side, we have: 0 = 0.0125r2+0.15r-36.
Now, we can apply the quadratic formula to solve for r.  Doing this, we find: r = 48 or -60.
In the context of the problem, the negative solution makes nosense, so r = 48 km/hr.
Cheers!

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