Question

Shelley and Emmy have collected a total of 275 butterflies. Shelley has 50 butterflies more than twice the number of butterflies that Emmy has. Which system of equations can be used to find s, the number of butterflies that Shelley has, and e, the number of butterflies that Emmy has?

Answer 1

To find the number of butterflies that Shelley and Emmy have, we can set up a system of equations based on the given information: s = 2e + 50 and s + e = 275. Solving this system, we find that Shelley has 200 butterflies and Emmy has 75 butterflies.

Step-by-step explanation:

To solve this problem, we can set up a system of equations based on the given information:

Let s be the number of butterflies that Shelley has and e be the number of butterflies that Emmy has.

The problem states that Shelley has 50 butterflies more than twice the number of butterflies that Emmy has. This can be expressed as:

s = 2e + 50

The problem also states that Shelley and Emmy have collected a total of 275 butterflies. This can be expressed as:

s + e = 275

Now we have a system of two equations:

s = 2e + 50

s + e = 275

We can solve this system using substitution or elimination method.

Let's solve it using the substitution method.

From the first equation, we can rearrange it to express e in terms of s:

e = (s - 50) / 2

Substitute this value of e in the second equation:

s + (s - 50) / 2 = 275

Multiply through by 2 to eliminate the fraction:

2s + s - 50 = 550

Combine like terms:

3s - 50 = 550

Add 50 to both sides:

3s = 600

Divide by 3:

s = 200

Now substitute this value of s in the first equation to find e:

200 = 2e + 50

Subtract 50 from both sides:

150 = 2e

Divide by 2:

e = 75

Therefore, Shelley has 200 butterflies (s = 200) and Emmy has 75 butterflies (e = 75).