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<h3>
Answer: 19 dimes</h3>
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Work Shown:
d = number of dimes
q = 32-d = number of quarters
$5.15 = 515 cents
10d+25q = 515
10d+25(32-d) = 515
10d+800-25d = 515
-15d+800 = 515
-15d = 515-800
-15d = -285
d = -285/(-15)
d = 19
There are 19 dimes. You can stop here if you want.
q = 32-d = 32-19 = 13
There are 13 quarters
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Check:
1 dime = 10 cents
19 dimes = 19*10 = 190 cents
1 quarter = 25 cents
13 quarters = 13*25 = 325 cents
total value = 190 cents + 325 cents = 515 cents = $5.15
The answer is confirmed.
First, let's see if we can rewrite this word problem a little bit more mathematically. We won't get to mathy or technical so no worries. We just want to look at it in a more straightforward way, if we can.
Train A's mph plus Train B's mph summed equal 723.5 mph. Train A's mph is greater than Train B's mph by 12.5 mph.
So what should we do to solve this problem? Since we are dealing with two of something and we know the value of the two combined, it might make sense to start by dividing that value by 2.
723.5 / 2 = <em /> 361.75. If the two trains were travelling at the same speed, we would be done. Unfortunately, they are not so we need to think about this some more.
Train A is going 12.5 mph faster than Train B. Let's rewrite.
Train A mph = 12.5 + 361.75 = 374.25 Okay, so Train A is travelling at a speed of 374.25 mph. So we're done right? Not exactly. We are asked to fing the speeds of BOTH trains. How do we find the speed of Train B? We have added a portion of the combined total to Train A. It seems to follow, then, we should probably subtract the same portion from Train A. What are we going to do? You guessed it! Rewrite.
Train B mph = 361.75 - 12.5 = 349.25 HA HA! We seem to have figured it out. Let's do one last thing to check our work. Let's add the two trains' speeds together. If we did this right, we should get our summed value of 723.5 mph
374.25 + 349.25 = 723.5
Pat yourself on the back! We did it!
374.25 + 349.25 =
Boom ha do boop bam pow oof big dude oof mousse oof sorry I couldn’t help ya son
