help please :)
1.) 3 years ago, Vin’s age is 3 times the age of Paul. At the present, Vin’s age is twice the age of Paul. What would be their age 3 years from now if the sum of their present age is 18?
2.) Willie bought a jacket for 26.86 pesos. The jacket’s price had been discounted by 15%. What was the sale price of the jacket before the discount?
2) 100%-15% = 85%
85/100 = 0.85
26.86/0.85= sales price
3 years ago:
Paul was X yrs. old.
Vin was 3x yrs. old.
At the present:
Paul is x+3 yrs. old.
Vin is 3x+3 yrs. old.
x+3 + 3x+3 = 18.
4x = 12.
X = 3.
Paul = x+3 = 3+3 = 6 yrs. old.
Vin = 3x+3 = 3*3 + 3 = 12 yrs. old.
3yrs. from now:
Paul = 6+3 = 9 yrs. old.
Vin = 12+3 = 15 yrs. old.
1.) To solve the first problem, let's assign variables to Vin's and Paul's ages. Let's say Vin's current age is V and Paul's current age is P.
According to the problem, three years ago, Vin's age was 3 times the age of Paul. So, we can write the equation: V - 3 = 3(P - 3).
At the present, Vin's age is twice the age of Paul. We can write the equation: V = 2P.
We are also given that the sum of their present ages is 18. We can write another equation: V + P = 18.
Now, we have a system of equations:
Equation 1: V - 3 = 3(P - 3).
Equation 2: V = 2P.
Equation 3: V + P = 18.
To solve this system, we can use substitution or elimination method. Let's use substitution method.
From Equation 2, we can express V in terms of P: V = 2P.
Substituting this value of V in Equation 3, we get: 2P + P = 18.
Combining like terms, we have: 3P = 18.
Dividing both sides by 3, we find: P = 6.
Substituting this value of P in Equation 2, we get: V = 2(6) = 12.
Therefore, Vin's current age is 12 and Paul's current age is 6.
To find their ages 3 years from now, we add 3 to both ages. So, Vin's age would be 12 + 3 = 15, and Paul's age would be 6 + 3 = 9.
Therefore, their ages 3 years from now would be 15 and 9.
2.) To solve the second problem, we need to find the original price of the jacket before the discount. Let's assign a variable to the original price. Let's say the original price is X.
According to the problem, the jacket's price had been discounted by 15%. This means the sale price is 85% of the original price (100% - 15% = 85%).
We can write this as an equation: 85% of X = 26.86 pesos.
To find 85% of X, we can convert the percentage to decimal form. 85% is written as 0.85.
The equation now becomes: 0.85X = 26.86.
To find X, we divide both sides of the equation by 0.85: X = 26.86 / 0.85.
Evaluating this expression, we find that the original price of the jacket before the discount is approximately 31.66 pesos.
Therefore, the sale price of the jacket before the discount was approximately 31.66 pesos.