During science class, teo, carson, and dhakir measure the length of their bean sprouts. carson’s sprout is 0.9 times the length of teo’s, and dhakir’s is 1.08 times the length of teo’s. whose bean sprout is the longest? the shortest? explain your reasoning.

The longest is Dhakir’s sprout

The shortest is Carson’s sprout

Step-by-step explanation:

Let

x > the length of Carson’s sprout

y > the length of Teo’s sprout

z > the length of Dhakir’s sprout

we know that

x=0.9y > equation A

z=1.08y > equation B

so

Express all quantities as a function of the variable y

The length of Carson’s sprout is 0.9y  (equation A)

The length of Teo’s sprout is y

The length of Dhakir’s sprout is 1.08y (equation B)

Compare

1.08y > y > 0.9y

therefore

The longest is Dhakir’s sprout

The shortest is Carson’s sprout

step-by-step explanation:

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: