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melisa1 [442]
3 years ago
10

Seiji and gavin both worked hard over the summer. Together they earned a total of $425. Gavin earned $25 more than seiji.

Mathematics
1 answer:
dlinn [17]3 years ago
7 0
S + g = 425
g = s + 25...these 2 equations are ur system of equations

s + (s + 25) = 425
2s + 25 = 425
2s = 425 - 25
2s = 400
s = 400/2
s = 200 <== what Seiji earned

g = s + 25
g = 200 + 25
g = 225 <=== what Gavin earned

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<h3>Answer: LCM = 132</h3>

===================================================

Work Shown:

LCM = least common denominator

List out the prime factorization of each denominator

  • 6 = 2*3
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So we have the list of primes 2,3, and 11 that help form the denominators when we multiply some of them together.

The prime 2 shows up at most twice, so 2*2 = 4 is a factor of the LCM

The prime 3 shows up at most one time, meaning 3 is also a factor

The prime 11 shows up at most one time, so 11 is another factor

Multiply these factors to get 4*3*11 = 12*11 = 132

The LCM is 132

---------------------

Another Approach:

Focus on 1/6 and 10/11 for now. The LCM is 66 because 6*11 = 66. We simply multiply the denominators together. Then we divide over the GCF 1 to get 66/1 = 66.

The LCM of 1/6 and 10/11 is 66

The fractions 1/6 and 10/11 are equivalent to 11/66 and 60/66 respectively

The original list of fractions updates to 11/66, 60/66, 5/12

We've gone from 3 different denominators to now 2 different denominators.

Repeat the steps of multiplying the denominators and dividing by the GCF

66*12 = 792

792/(gcf of 66 and 12) = 792/6 = 132

So the LCM of all the fractions is 132.

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