1.) If the perimeters of the triangle and the rectangle are the same, then this means
[tex]2(3x - 3) + 2(x - 3) = 2(2x - 1) + 2x[/tex]
First distribute:
2(3x - 3) = 6x - 6
2(x - 3) = 2x - 6
Let's look at the bolded coefficients:
6x - 6 + 2x - 6 = 4x - 2 + 2x
= 8x - 6 - 6 = 6x - 2
Isolate the variables:
8x - 6x = -12 - 2
2x = 10, so x = 5
Plug in the variables:
Rectangle: 2(3(5) - 3) + 2(5 - 3)
= 2(15 - 6) + 2(2)
= 24 + 4 = 28 feet
Triangle: 2(2(5)-1) + 2(5)
= 2(9) + 10 = 18 + 10 = 28 feet
Claire purchased 28 feet of fencing.
2.) Celia: 1200 calories a day, increases by 100 each day, so 1200 + 100d.
Ryan: 3230 calories per day, decreases it by 190 each day, so 3230 - 190d.
For the variables to equal the same amount:
[tex]1200 + 100d = 3230 - 190d[/tex]
Let's isolate the variables:
1200 - 3230 = -190d - 100d, since there is no such thing as negative 290 days,
290d = 2030
d = [tex]\frac{2030}{190}[/tex], so d = seven days.
Plug in variable:
Celia: 1200 + 100(7) = 1900 calories
Ryan: 3230 - 190(7) = 1900 calories.
In seven days, they will both be consuming 1900 calories.
3.) 800 + 16h = 720 + 21h
Isolate the variable:
800 - 720 = -16h + 21h
80 = 5h, which means 16 hours.
4.) 2500 + 150m = 3000 + 125m
Isolate the variable:
3000 - 2500 = 150m - 125m
500 = 25m
[tex]\frac{500}{25}[/tex] is 20 months.
5.) [tex]200 + 45m = 50 + 55m[/tex]
200 - 50 = 55m - 45m
150 = 10m
m = 15 months.
6.) 200 + 45(15) = 200 + 675 = $875
7.) [tex]200 + 45m = 20 + 60m[/tex]
= 200 - 20 = 60m - 45m
180 = 15m
[tex]\frac{180}{15}[/tex] = 12, so it will take 12 months.
