In order to encourage his son in the study of

garnentas3m

garnentas3m

Answered question

2021-12-18

In order to encourage his son in the study of Algebra, a father promised the son P8.00 for every problem solved correctly and to fine him P5.00 for each incorrect solution. After 26 problems, neither owed any amount to the other. How many problems did the boy solve correctly?

Answer & Explanation

raefx88y

raefx88y

Beginner2021-12-19Added 26 answers

Given data, 
price for correct answer =8(c) correct 
price for incorrect answer =5(w)-wrong 
No. of problems =26
No. of problems =no. of correct problems+ 
no. of wrong problems 26=c+w 
In end, neither owed any money. 
So, 8c5w=0 
Solution: 
The Equation are 
c+w=26 
8c5w=0 
c+w=26×55c+5w=130 
8c-5w=0 
5c+5w=130 
13c=130 
C=13013=10
c=10 
c+w=26 
w=26c=2610=16 
w=16 
The Boy solve the problem correctly 10.

Raymond Foley

Raymond Foley

Beginner2021-12-20Added 39 answers

Let xnr of correct solution
ynr of wrong solution
8x5y=0
x+y=26
8(26y)5y=0
2088y5y=0
13y=208
y=16
x=10
The boy got 10 correct answers.
To check
8(10)5(16)=0
8080=0
0=0
Don Sumner

Don Sumner

Skilled2021-12-28Added 184 answers

Step 1 Given: For correct solution by gets P8.00 For incorrect solution, he loses P5.00 Step 2 Suppose x shows correct solution and y shows wrong solutions and he solved a total of 26 problems, therefore, x+y= 26(1) For the correct solution, he getting 8.00 so 8x and for the incorrect solution, he loses 5.00 so -5y After 26 problems he has an amount 0 therefore, 8x -5y =0 (2) Solving equation (1) and (2) together Multiply equation (1) by 5 5x+5y= 130 (3) Add equation (2) and (3) (8x -5y )+(5x+5y)=130+0 (8x+5x)+(5y-5y)=130 13x+0=130 13x=130 x=10 Therefore, the boy solved 10 problems correctly.

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