Answer: A) 18.2 minutes
B) 4.5 minutes.
Step-by-step explanation:
A) Maxine can mow one lawn in 24 minutes, so the rate of work is:
1/24 of the lawn per minute.
Sammie can mow one lanw in 36 minutes, so the rate of work is:
1/36 of the lawn per minute.
The amount of the lawn that each has left to lawn by the minute x is:
Maxine = 1 -(1/24)*x
Sammie = 1 - (1/36)*x
we want to find the value of x such that:
2*(1 - (1/24)*x) = 1 - *(1/36)*x
which means that the amount that Sammie has left is two times the amount that Maxine has left to mow.
2 - (1/12)*x = 1 - (1/36)*x
2 - 1 = (1/12 - 1/36)*x
1/0.055 = x = 18.2
by the minute 18.2
B) Similar to before, here the rates are:
For Maxine, R = 1/6
For Sammie, R = 1/9
The amount they have left to mow by minute x is:
Maxine = 1 - (1/6)*x
Sammie = 1 - (1/9)*x
We want to solve, similar to before.
2( 1 - (1/6)*x) = 1 - (1/9)*x
2 - (1/3)*x = 1 - (1/9)*x
2 - 1 = (1/3 - 1/9)*x
1 = (2/9)*x
1*9/2 = x = 4.5
So here the solution is 4.5 minutes. Hope this helps
X = y - 1
Hope that helps! :)
Lets say that variable x=total number of hotdogs, and variable y=total number of drinks. Our first equation will calculate the total cost.
2x+1y=11. We are multiplying the price by the total number of each item then adding them together, since they spent a total of $11. Our second equation will calculate the number of items.
x+y=8.
To solve, we will isolate x in the second equation. x=8-y We will substitute that for x in the first equation. 2(8-y)+1y=11 Distributive property. 16-2y+1y=11 Combine like terms. 16-y=11 Isolate y to solve. y=5 Then we plug y into the second equation and solve for x. x+5=8 Subtract 5 from both sides. x=3