I need help on two problems I would like if you went step by step with the problem with me and then let me figure out the answer.
If, Tonya and Toya have $15.25 together and Tonya had 25 cents more than Toya, how much does each have?
Second question:
Bruce is 7 years older than his sister Pilar. The sum of their ages is 1 less than 3 times Pilar's age. How old is each.
Show equations for both
First problem:
X1 + X2 = 15.25
X1 - X2 = 0.25
2 X1 = 15.50
X1 = 7.75
X2 = X1 - 0.25 = 7.50
Second problem:
B - P = 7
B + P = 3P -1
B - 2P = -1
P = 8
B = P+7 = 15
Sure, let's work through the first problem step by step:
We are given that Tonya and Toya have a total of $15.25 together. Let's represent the amount of money Tonya has as X1 and the amount of money Toya has as X2.
So we can write the first equation as:
X1 + X2 = 15.25
We are also told that Tonya has 25 cents more than Toya. This means that Tonya's amount (X1) is 25 cents (or $0.25) more than Toya's amount (X2). Mathematically, this can be represented as:
X1 - X2 = 0.25
Now we have a system of two equations:
Equation 1: X1 + X2 = 15.25
Equation 2: X1 - X2 = 0.25
To solve this system, we can use the method of substitution or elimination. Let's use elimination.
To eliminate the variable X2, we can multiply Equation 2 by -1:
-1(X1 - X2) = -1(0.25)
- X1 + X2 = -0.25
Now we can add Equations 1 and -X1 + X2:
(X1 + X2) + (-X1 + X2) = 15.25 + (-0.25)
2X2 = 15.00
Divide both sides by 2 to isolate X2:
X2 = 15.00 / 2
X2 = 7.50
Now that we know X2, we can substitute this value back into equation 1 to find X1:
X1 + 7.50 = 15.25
X1 = 15.25 - 7.50
X1 = 7.75
So Tonya has $7.75 and Toya has $7.50.
Now let's move on to the second question, step by step:
We are given that Bruce is 7 years older than his sister Pilar. Let's represent the age of Pilar as P and the age of Bruce as B.
So we can write the first equation as:
B - P = 7
We are also given that the sum of their ages is 1 less than 3 times Pilar's age. Mathematically, this can be represented as:
B + P = 3P - 1
Now we have a system of two equations:
Equation 1: B - P = 7
Equation 2: B + P = 3P - 1
To solve this system, let's use the method of substitution.
From Equation 1, we can isolate B:
B = P + 7
Now substitute this expression for B in Equation 2:
(P + 7) + P = 3P - 1
Simplify:
2P + 7 = 3P - 1
Subtract 2P from both sides:
7 = P - 1
Add 1 to both sides:
8 = P
Now that we know Pilar's age is 8, we can substitute this value back into Equation 1 to find Bruce's age:
B - 8 = 7
B = 7 + 8
B = 15
So Bruce is 15 years old and Pilar is 8 years old.
I hope this helps! Let me know if you have any more questions.