Mika can eat 212121 hot dogs in 666 minutes. she wants to know how many minutes (m)(m)left parenthesis, m, right parenthesis it would take her to eat 353535 hot dogs if she can keep up the same pace. how many minutes would mika need to eat 353535 hot dogs?

10 minutes

Step-by-step explanation:

1 / 7

We're dealing with a proportional relationship, so each ratio of hot dogs to minutes must be equivalent.

Hint #22 / 7

Here's one way to write the proportion:

\dfrac{21 \text{ hot dogs}}{6\text{ mins}} = \dfrac{35\text{ hot dogs}}{m\text{ mins}}

6 mins

21 hot dogs

​  =

m mins

35 hot dogs

​  start fraction, 21, space, h, o, t, space, d, o, g, s, divided by, 6, space, m, i, n, s, end fraction, equals, start fraction, 35, space, h, o, t, space, d, o, g, s, divided by, m, space, m, i, n, s, end fraction

Hint #33 / 7

Let's solve for mmm:

\dfrac{21 \text{ hot dogs}}{6\text{ mins}} = \dfrac{35\text{ hot dogs}}{m\text{ mins}}

6 mins

21 hot dogs

​  =

m mins

35 hot dogs

​  start fraction, 21, space, h, o, t, space, d, o, g, s, divided by, 6, space, m, i, n, s, end fraction, equals, start fraction, 35, space, h, o, t, space, d, o, g, s, divided by, m, space, m, i, n, s, end fraction

m \cdot 21 = 35 \cdot 6\qquadm⋅21=35⋅6m, dot, 21, equals, 35, dot, 6, space[Explain]

\dfrac{21}{6 } = \dfrac{35}{m}

start fraction, 21, divided by, 6, end fraction, equals, start fraction, 35, divided by, m, end fraction

m\cdot\dfrac{21}{6 } = \dfrac{35}{\cancel{m}} \cdot \cancel{m}

mm

m\cdot \dfrac{21}{6} = 35

m, dot, start fraction, 21, divided by, 6, end fraction, equals, 35

\cancel{6} \cdot m\cdot \dfrac{21}{\cancel{6}} = 35 \cdot 6

66

m \cdot 21 = 35 \cdot 6m, dot, 21, equals, 35, dot, 6

Hint #44 / 7

21m = 21021m=21021, m, equals, 210

Hint #55 / 7

m = \dfrac{210}{21}m=

21

210

​             m, equals, start fraction, 210, divided by, 21, end fraction, space, space, space, space, space, space, space, space, space, space, space Divide both sides by 212121.

Hint #66 / 7

m = 10m=10m, equals, 10

Hint #77 / 7

Mika would need 101010 minutes to eat 353535 hot dogs.