# Word Problem - steps to solve

by Sylvia Pepe
(Lancaster, Lancashire, United Kingdom)

A school has 308 dictionaries. There are 3 infant classes and 4 junior classes. The junior classes need twice as many dictionaries as the infant classes. How many dictionaries can each infant and junior class have?

Please, could you help me to find out the different steps for this problem. I have got the answers but I will not get the steps they have done.

### Comments for Word Problem - steps to solve

 Feb 09, 2013 Word Problem by: Staff Answer Part I To answer this question, you will be solving a system of two linear equations. x = number of dictionaries for each infant class y = number of dictionaries for each junior class total number of dictionaries = 308 1st equation: Use this part of the problem statement to develop the 1st equation: A school has 308 dictionaries. There are 3 infant classes and 4 junior classes. number of dictionaries given to infant classes + number of dictionaries given to junior classes = total number of dictionaries number of dictionaries given to infant classes + number of dictionaries given to junior classes = 308 (number of infant classes) * x + (number of junior classes) * y = 308 3 * x + 4 * y = 308 3 x + 4 y = 308 2nd equation: Use this part of the problem statement to develop the 2nd equation: The junior classes need twice as many dictionaries as the infant classes. (each junior class will need twice as many dictionaries as each individual infant class) y = 2x (number of dictionaries for each junior class) = 2 * (number of dictionaries for each infant class) y = 2 * x y = 2 x System of Equations you must solve 1st equation: 3 x + 4 y = 308 2nd equation y = 2 x Solving for x and y This problem can be solved using either the substitution of elimination methods. I am going to demonstrate the solution using the substitution method. 1st equation 3 x + 4 y = 308 since y = 2 x, substitute 2 x wherever y appears in the 1st equation 3 x + 4 * (2x) = 308 3 x + 8 x = 308 now, solve for x 3 x + 8 x = 308 11 x = 308 11 x / 11= 308 / 11 x * (11 / 11)= 308 / 11 x * (1)= 308 / 11 x = 308 / 11 x = 28 dictionaries since you now know that x = 28, substitute 28 wherever x appears in the 1st equation 3 x + 4 y = 308 3 * 28 + 4 y = 308 84 + 4 y = 308 ---------------------------------------------------------------

 Feb 09, 2013 Word Problem by: Staff --------------------------------------------------------------- Part II complete the problem by solving for y 84 + 4 y = 308 84 + 4 y - 84 = 308 - 84 4 y + 84 - 84 = 308 - 84 4 y + 0 = 308 - 84 4 y = 308 - 84 4 y = 224 4 y / 4 = 224 / 4 y * (4 / 4) = 224 / 4 y * (1) = 224 / 4 y = 224 / 4 y = 56 dictionaries Final Answer: x (infant class) = 28 dictionaries y (junior class) = 56 dictionaries This system of equations can also be solved graphically ---------------------------------------------------- Check the result for accuracy x = 28 dictionaries y = 56 dictionaries 1st equation: 3 x + 4 y = 308 3 * 28 + 4 * 56 = 308 84 + 224 = 308 308 = 308, OK 2nd equation: y = 2 x 56 = 2 * 28 56 = 56, OK Thanks for writing. Staff www.solving-math-problems.com