Question

Kristen spent many days at the community pool last summer. She noticed that five out of fourteen flying insects she saw at the pool were mayflies. If Kristen saw fourteen flying insects at the pool one day, how many were mayflies? If, over several days, Kristen saw forty two flying insects, how many were mayflies? If, over a few weeks, Kristen saw thirty mayflies, how many flying insects did she see?

Answer 1

(a) 5 mayflies

(b) 15 mayflies

(c) 84 flying flies

Explanation:

Represent Mayflies with M and the total flying insects with F

The ratio can be represented as:

`M : F = 5 : 14`

Solving (a):

`F = 14`

Find M

Substitute 14 for F in
`M : F = 5 : 14`

`M : 14 = 5 : 14`

Convert to fraction

`(M)/(14) = (5)/(14)`

Multiply through by 14

`14 * (M)/(14) = (5)/(14) * 14`

`M = 5`

Solving (b):

`F = 42`

Find M

Substitute 42 for F in
`M : F = 5 : 14`

`M : 42 = 5 : 14`

Convert to fraction

`(M)/(42) = (5)/(14)`

Multiply through by 42

`42 * (M)/(42) = (5)/(14) * 42`

`M = (5)/(14) * 42`

`M=5*3`

`M= 15`

Solving (c):

`M = 30`

Find F

Substitute 30 for M in
`M : F = 5 : 14`

`30 : F = 5 : 14`

Convert to fraction

`(F)/(30) = (14)/(5)`

Multiply through by 30

`30 * (F)/(30) = (14)/(5) * 30`

`F = (14)/(5) * 30`

`F = 14*6`

`F = 84`