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1) Max drove for 3 hours before lunch. After lunch he drove 4 more hours and averaged 15 mph more than before lunch. If his total distance was 410 miles, then what was his average speed before lunch?

2)Becca has 15 coins consisting of dimes and nickels. The total value of the coins is $0.95. How many of each does she have?

3)Sam invested some money at 6% simple interest and some money at 10% simple interest.In the second investment he put $1000 more than he put in the first. If the income from both investments for 1 year was $340, then how much did he invest at each rate?

1) Take the speed before lunch as x mph.

This means the total distance would be 3x + 4(x+15) = 3x + 4x + 60 = 7x + 60.

Since we are given that this is 410 miles, we have 7x + 60 = 410.

Subtract 60 from both sides, giving only a 7x on the left side.

Divide both sides by 7 and get answer that sounds good for a car.

2) If she has 15 coins that are dimes and nickels, assume that there are x dimes.

If all the coins were nickels, the value would be 15*5c = 75c.

Given that we have x dimes, each dime increase that value by 5c, so the total value is 75 + 5x.

The equation is then 75 + 5x = 95,

To solve, subtract 75 from both sides, giving 5x = 20.

Divide both sides by 5, and that is the number of dimes.

3) Sam invested x at 6%. He invested x+1000 at 10%.

This means that the total earned is 0.06x + 0.10(x+1000) = 0.06x + 0.10x + 100.

That is the same as 0.16x + 100. If that is $340, that means 0.16x + 100 = 340.

If 100 is subtracted from both sides, that should gives 0.16x = 240.

Divide both sides by 0.16, and then you will have the value for x.

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