QuestionA clown weighs $60 \mathrm{lb}$ more than a trapeze artist, who is two-thirds the clown's weight. Find their weights. Choices: $110, 120, 125$ .

Studdy Solution

STEP 1

Assumptions1. The clown weighs60 lb more than the trapeze artist. . The trapeze artist weighs two thirds as much as the clown.

STEP 2

Let's denote the weight of the trapeze artist as $x$ (in lb). Therefore, according to the problem, the clown weighs $x +60$ lb.

STEP 3

According to the second condition, the trapeze artist weighs two thirds as much as the clown. We can write this as an equation $x = \frac{2}{3}(x +60)$

STEP 4

Now, we can solve this equation for $x$ . First, multiply both sides by3 to get rid of the fraction $3x =2(x +60)$

STEP 5

Expand the right side of the equation $3x =2x +120$

STEP 6

Subtract $2x$ from both sides of the equation $x =120$

STEP 7

So, the trapeze artist weighs120 lb. To find the weight of the clown, we can substitute $x =120$ into the equation $x +60$ $x +60 =120 +60$

STEP 8

Calculate the weight of the clown $x +60 =180$ So, the clown weighs180 lb.

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QuestionA clown weighs $60 \mathrm{lb}$ more than a trapeze artist, who is two-thirds the clown's weight. Find their weights. Choices: $110, 120, 125$ .

Studdy Solution

STEP 1

Assumptions1. The clown weighs60 lb more than the trapeze artist. . The trapeze artist weighs two thirds as much as the clown.

STEP 2

Let's denote the weight of the trapeze artist as $x$ (in lb). Therefore, according to the problem, the clown weighs $x +60$ lb.

STEP 3

According to the second condition, the trapeze artist weighs two thirds as much as the clown. We can write this as an equation $x = \frac{2}{3}(x +60)$

STEP 4

Now, we can solve this equation for $x$ . First, multiply both sides by3 to get rid of the fraction $3x =2(x +60)$

STEP 5

Expand the right side of the equation $3x =2x +120$

STEP 6

Subtract $2x$ from both sides of the equation $x =120$

STEP 7

So, the trapeze artist weighs120 lb. To find the weight of the clown, we can substitute $x =120$ into the equation $x +60$ $x +60 =120 +60$

STEP 8

Calculate the weight of the clown $x +60 =180$ So, the clown weighs180 lb.

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QuestionA clown weighs 60lb60 \mathrm{lb}60lb more than a trapeze artist, who is two-thirds the clown's weight. Find their weights. Choices: 110,120,125110, 120, 125110,120,125.

Studdy Solution

STEP 1

Assumptions1. The clown weighs60 lb more than the trapeze artist. . The trapeze artist weighs two thirds as much as the clown.

STEP 2

Let's denote the weight of the trapeze artist as xxx (in lb). Therefore, according to the problem, the clown weighs x+60x +60x+60 lb.

STEP 3

According to the second condition, the trapeze artist weighs two thirds as much as the clown. We can write this as an equationx=23(x+60)x = \frac{2}{3}(x +60)x=32​(x+60)

STEP 4

Now, we can solve this equation for xxx. First, multiply both sides by3 to get rid of the fraction3x=2(x+60)3x =2(x +60)3x=2(x+60)

STEP 5

Expand the right side of the equation3x=2x+1203x =2x +1203x=2x+120

STEP 6

Subtract 2x2x2x from both sides of the equationx=120x =120x=120

STEP 7

So, the trapeze artist weighs120 lb. To find the weight of the clown, we can substitute x=120x =120x=120 into the equation x+60x +60x+60x+60=120+60x +60 =120 +60x+60=120+60

STEP 8

Calculate the weight of the clownx+60=180x +60 =180x+60=180So, the clown weighs180 lb.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionA clown weighs $60 \mathrm{lb}$ more than a trapeze artist, who is two-thirds the clown's weight. Find their weights. Choices: $110, 120, 125$ .

Let's denote the weight of the trapeze artist as $x$ (in lb). Therefore, according to the problem, the clown weighs $x +60$ lb.

According to the second condition, the trapeze artist weighs two thirds as much as the clown. We can write this as an equation $x = \frac{2}{3}(x +60)$

Now, we can solve this equation for $x$ . First, multiply both sides by3 to get rid of the fraction $3x =2(x +60)$

Expand the right side of the equation $3x =2x +120$

Subtract $2x$ from both sides of the equation $x =120$

So, the trapeze artist weighs120 lb. To find the weight of the clown, we can substitute $x =120$ into the equation $x +60$ $x +60 =120 +60$

Calculate the weight of the clown $x +60 =180$ So, the clown weighs180 lb.