Int. Alg. word probs: number of coins, distance, angles, etc

[SHARON BUCHANAN]

1) Solving money denomination: There are thirty-nine coins. Some are pennies, and the rest are dimes. The total value of the coins is $2.64. How many of each denomination of coin do you have?

Let x represent the number of pennies. Then 39 - x represents the number of dimes. Then:

. . .0.01x
. . .0.39(39 - x)
. . .0.01x + 0.39(39 - x)

I can't figure out what to do next.

2) A train leaves Kansas City and travels north at 85 kph (kilometers per hour). Another train leaves at the same time and travels south at 95 kph. How long will it take before they are 315 km apart?

I don't even know how to begin to do this problem.

3) Find the measure of each angle in the triangle, given the following angle-measure expressions:

. . .angle 1: (2x + 7)°
. . .angle 2: (x + 61)°
. . .angle 3: x°

How would I find the value of x?

4) Find four consecutive integers such that the sum of the first three is 54 more than the fourth.

How would I get started on this one?

Thank you.
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Edited by stapel -- Reason for edit: removing ALL CAPS

 

[stapel]

1) Your expressions for the numbers of coins is fine, but (hint) what is the meaning of "0.01x"? What is the meaning of "0.39(39 - x)"? Where do you take into account the value of the coins?

2) Until we know how far apart the trains were when they started, I'm afraid this is unanswerable. (We can't know when they are 315 km apart if we don't know how far apart they were at the beginning.)

3) Hint: What is the angle-measure sum of any triangle?

4) If the first integer is "1", what is the "next" integer? If the first integer is "5", what is the "next" integer? How far apart were the first integers and the next integers? With that in mind, if the first integer is "x", what is the "next" integer?

Eliz.

 

[Denis]

Re: Int. Alg. word probs: number of coins, distance, angles,

2) A train leaves Kansas City and travels north at 85 kph (kilometers per hour). Another train leaves at the same time and travels south at 95 kph. How long will it take before they are 315 km apart?

After 1 hour (60 minutes), the trains will be 85 + 95 = 180 km apart.

So if 180 takes 60 minutes, how long does 315 take?

 

[SHARON BUCHANAN]

WOULD IT BE 1 HR AND 45 MINUTES

 

[Denis]

Of course, Sharon: 60 / 180 * 315 = 105 = 1 hour 45 minutes; good work!

Now go change your coin thing to .10(39 - x) :wink: