leylee21993 said:
I need help solving a few word problems
1. Sarah has 260 coins with a total value of $35.00. The coins are dimes and quarters. How many of each coin does she have?
2. Suppose you invest $12,000 in two accounts paying 8% and 6% interest annually. How much money do you have in each account if the total interest earned for a year is $880?
3. A truck travels 300 miles in the same amount of time it takes a car traveling 5 miles per hour slower than the truck to go 275 miles. What is the speed of the truck?
In 1 when naming things, be sure to distinguish the difference between the
number of dimes and the
value of the coins. For instance, if you make the statement "Let d represent the number of dimes" then you know that "0.10d" represents the value of the dimes, expressed in dollars. If you want to represent the value of the dimes in cents, then it is "Let 10d represent the value of the dimes in cents." If you choose the latter, then you have to change the $35.00 to 3500 cents. Likewise if q represents the number of quarters, then 25q represents the value of quarters
in cents. Of course you know that d+q=260.
Similarly, in 2 you have to distinguish between the value of the original investment and the value of the annual interest.
For instance if x represents the amount of money invested at 8%, the the amount of interest earned on that portion of the overall investment is .08x. If y represents the amount of money invested at 6%, then .06y represents the amount of interest on that amount.
In 3, you could name things this way. (Always take the time to write your original naming of thing all the way out).
Let r represent the rate of the truck. Then r-5 will represent the rate of the car. Since they are both on the road for the same amount of t, you can say "Let t represent the length of time they are on the road."
Now, you can use the formula rt = d (rate X time = distance) to build two equations and solve simultaneously.
Always remember to check your answers by plugging the results back into the original word problems, and use arithmetic to see if they tell the truth.
