Question

Please help im desperate here :/

Answer 1

1.) If the perimeters of the triangle and the rectangle are the same, then this means

$2(3x - 3) + 2(x - 3) = 2(2x - 1) + 2x$

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:

$1200 + 100d = 3230 - 190d$

Let's isolate the variables:

1200 - 3230 = -190d - 100d, since there is no such thing as negative 290 days,

290d = 2030

d = $\frac{2030}{190}$, 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

$\frac{500}{25}$ is 20 months.

5.) $200 + 45m = 50 + 55m$

200 - 50 = 55m - 45m

150 = 10m

m = 15 months.

6.) 200 + 45(15) = 200 + 675 = $875

7.) $200 + 45m = 20 + 60m$

= 200 - 20 = 60m - 45m

180 = 15m

$\frac{180}{15}$ = 12, so it will take 12 months.