Anna burned 15 calories per minute running for x minutes and 10 calories per minute hiking for y minutes. She spent a total of 60 minutes running and hiking and burned 700 calories. The system of equations shown below can be used to determine how much time Anna spent on each exercise. What is the value of x, the minutes Anna spent running? * 15x + 10y = 700 / x + y = 60
x+y=60
15x+10y=700
Yes, your equations are correct.
multipy the first equation by 20, then subtract it from the second.
To solve this system of equations, we can use the elimination or substitution method. Let's explain both methods and then apply them to the given equations.
1. Elimination method:
To solve a system of equations using the elimination method, we want to eliminate one variable by adding or subtracting the equations. Here's how:
- First, let's multiply the second equation by 15 to make the coefficients of the x terms in both equations the same:
15(x + y) = 15(60)
15x + 15y = 900
- Now, we can subtract the first equation from the modified second equation:
(15x + 15y) - (15x + 10y) = 900 - 700
5y = 200
- Divide both sides of the equation by 5 to solve for y:
y = 40
- Now, substitute the value of y back into either of the original equations. Let's use the first equation:
15x + 10y = 700
15x + 10(40) = 700
15x + 400 = 700
- Subtract 400 from both sides of the equation:
15x = 700 - 400
15x = 300
- Finally, divide both sides of the equation by 15 to solve for x:
x = 20
Therefore, the value of x, the minutes Anna spent running, is 20 minutes.
2. Substitution method:
To solve a system of equations using the substitution method, we want to substitute one equation into the other to solve for one variable. Here's how:
- Rewrite the second equation as y = 60 - x
- Substitute this expression for y in the first equation:
15x + 10(60 - x) = 700
15x + 600 - 10x = 700
5x + 600 = 700
- Subtract 600 from both sides of the equation:
5x = 700 - 600
5x = 100
- Divide both sides of the equation by 5 to solve for x:
x = 20
Therefore, the value of x, the minutes Anna spent running, is 20 minutes.
In both cases, we get the same result: Anna spent 20 minutes running (x = 20).