Question 1121178: Helen has P2.40 in 25 cents and 5 cents. She has a total of 24 coins. How many 25 cents coins and how many 5 cents coins does she have? Answer by ikleyn(52786) (Show Source):
You can start from the system of two equations in two unknowns
x + y = 24 (1) (counting coins)
5x + 25y = 240 (2) (counting cents)
Then you can multiply the first equation by 5 (both sides) to get the system in the equivalent form
5x + 5y = 120 (1')
5x + 25y = 240 (2')
Now you can subtract equation (1') from equation (2'). In this way, you exclude the unknown x, and you get
a single equation for the unknown y:
25y - 5y = 240 - 120
20y = 120
y = = 6.
Answer. 6 quarters and (24-6) = 18 nickels.
Check. 6*25 + 18*5 = 240 cents. ! Correct !
Solved. // The method I used to solve the system is called the "Elimination method".
So, on the way, you learned how to solve the system of equations using the Elimination method.
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
Read them attentively and become an expert in this field.
