Rational equations are solved by determining excluded values, multiplying by the LCD, solving the resulting linear equation, and eliminating extraneous solutions
In an integer between 10 and 100, the unit’s digit is 3 greater than the ten’s digit. Find the integer, if it is 4 times as large as the sum of its digits.
A certain two digit number is equal to 9 times the sum of its digits. If 63 were subtracted from the number the digits would be reversed. Find the number.
The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.
A change purse contains an equal number of pennies, nickels and dimes. The total value of the coins is $1.44. How many of each type does the purse contain?
Mary has $3.00 in nickels, dimes and quarters. If she has twice as many dimes as quarters and five more nickels than dimes, how many coins of each type does she have?
An ambitious 14-year old has saved $1,800 from chores and odd jobs around the neighborhood. If he puts this money into a CD that pays a simple interest rate of 4% a year, how much money will he have in his CD at the end of 18 months?
Theresa earns a full athletic scholarship for college, and her parents have given her the $20,000 they had saved to pay for her college tuition. She decides to invest that money with an overall goal of earning 11% interest.
A mechanic is working on the coolant system of a vehicle with a capacity of 11.0 liters. Currently the system is filled with coolant that is 45% ethylene glycol. How much fluid must be drained and replaced with 100% ethylene glycol so that the system will be filled with coolant that is 60% ethylene glycol?
For a certain experiment, a student requires 100 ml of a solution that is 8% HCl. The storeroom has only solutions that are 5% and 15% HCl.