1. Sarah has a collection of nickels, dimes, and quarters worth $22.25. She has
ID: 2335503 • Letter: 1
Question
1. Sarah has a collection of nickels, dimes, and quarters worth $22.25. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?2. Abby has 47 coins, consisting only of dimes and quarters, worth $8.45. How many dimes and how many quarters does she have?
3. Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 150 miles per hour and the other at 490 miles per hour, how long will it take for them to be 3000 miles apart? 1. Sarah has a collection of nickels, dimes, and quarters worth $22.25. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?
2. Abby has 47 coins, consisting only of dimes and quarters, worth $8.45. How many dimes and how many quarters does she have?
3. Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 150 miles per hour and the other at 490 miles per hour, how long will it take for them to be 3000 miles apart?
2. Abby has 47 coins, consisting only of dimes and quarters, worth $8.45. How many dimes and how many quarters does she have?
3. Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 150 miles per hour and the other at 490 miles per hour, how long will it take for them to be 3000 miles apart?
Explanation / Answer
1) Let number of nickels be x;
Value 1 =5x cents
No. of dimes is "x+10"; thus Value 2 = 10x + 100 cents
No. of quarters: 2(x+10) = 20x + 20; thus Value 3: 25(2x + 20) = 50x + 500 cents
Value 1 + Value 2 + Value 3 = 22.25
5x + 10x+100+50x+500 = 2225
65x +600 = 2225
x = 1625/65 = 25
Thus, Number of nickels = 25
Number of dimes = 25 + 10 = 35
Number of quarters = 2*25 + 20 = 70
2)
Equation: d + q = 47
or, 10d+25q= 845 cents
Now two equation are:
10d + 10q = 470 cents -----(1)
10d+25q= 845 cents -----(2)
Subtracting 1st from 2nd to compute for "q":
15q = 375
q = 25
Thus number of quarters equals 25 and number of dimes equals 22 (=47-25)
3) 3000 / (150 + 490) = 4.69 hours
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