02 An introduction to problem solving
Grant is thinking of two numbers. He says that one of the numbers is four times the other number and the sum of numbers is 55. What
are the numbers?
The two numbers are ___ and ___.
The first number is 44 and the second number is 11.
2.) the sum of three consecutive integers is 57. Find the integers.
Let x = the first integer
Then x+1 = the second integer
Then x+2 = the third integer
The integers are 18, 19 and 20.
3.) going into the final exam which will count as two tests, Brooke has test scores of 77, 82, 72, 59 and 94. What score does Brooke need
on the final in order to have an average score of 80.
Brook needs a score of ___.
1.) Let x = Brooke's final exam score
2.) skip
3.) test scores / 7 = her average score
4.) 384 + 2x / 7 = 80
5.) Brooke needs a score of 88.
An inheritance of $1,400,000 is to be divided among Scott, Alice, and Tricia in the following manner. Alice is to receive 6/7 of what Scott
gets, while Tricia gets 1/7 of what Scott gets. How much does each receive.
Scott gets $______
1.) let x = money Scott receives
2.) then 6/7 x = Alice's money
then 1/7 x = Tricia's money
3.) Scott's money + Alice's money + Tricia's money = the total
A bank loaned out $20,000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled
$2000, how much was loaned at 7%.
How much was loaned at 7%?
1.) let x = # of $ loaned at 7%
2.) then 20,000-x = # of $ invested at 17%
3.) interest paid at 7% + the interest paid at 17% = the total interest
Interest = principle x rate x time
=
Interest = principle x rate x time
=
10.) carol has been saving quarters and dimes. She opened up the piggy bank and determined that it contained 14 coins worth $2.30.
Determine how many dimes and quarters were in the piggy bank.
There were ___ dimes.
There were ___ quarters.
1.) let x = the number of dimes
2.) then 14-x = the number of quarters.
3.) the value of the dimes + the value of the quarters = the total value.