In Mr. Elliot’s garden, 1/ 8 of the flowers are red, 1/ 4 of them are purple, and 1/ 4 of the remaining flowers are pink. If there are 128 flowers, how many flowers are pink?

Question

In Mr. Elliot’s garden, 1/

8

 of the flowers are red, 1/

4

 of them are purple, and 1/

4

 of the remaining flowers are pink.

If there are 128 flowers, how many flowers are pink?

Answer 1

Hi Journee!

Total flowers = 128

Red flowers = 1/8 of total flowers ---> 1/8 x 128 = 16

Purple flowers = 1/4 of total flowers ---> 1/4 x 128 = 32

Remaining flowers = Total flowers - Red flowers - Purple flowers

= 128 - 16 - 32

= 80

1/4 of Remaining flowers are pink,

so Pink flowers = 1/4 x Remaining flowers

= 1/4 x 80

= 20

Answer 2

Hi Journee,

This problem is definitely a multi-step one.

Also, there are different ways to approach the problem.

We can "work" all the fractions first and determine what fraction of the total are pink and then apply that fraction to the 128 total.

or

We can apply the given fractions to determine the subtotals and subtract them from the 128 total.

LET'S DO BOTH.

Subtract 1/8 and 1/4 from the whole (1); 1 - 1/8 - 1/4

Convert the fractions to have a common denominator of 8; 8/8 - 1/8 - 2/8

Subtract the numerators; (8 - 1 - 2)/8 = 5/8.

This means 5/8 of the flowers are not red or purple.

Next, we find 1/4 of 5/8 by multiplying the fractions; 1/4 × 5/8 = 5/32

This means that 5/32 of the flowers are pink.

Multiply 128 by 5/32; 128 × 5/32 = 20.

There are 20 pink flowers.

Now let's try the other approach.

This time we will first determine how many flowers are red, how many are purple, and subtract them from the total.

If 1/8 of the flowers are red then, 1/8 × 128 = 16

If 1/4 of the flowers are purple then, 1/4 × 128 = 32

The "remaining" flowers can now be found by subtracting; 128 - 32 - 16 = 80.

Lastly, we need to determine 1/4 of 80; 1/4 × 80 = 20.

Either way we get the same answer.

There are 20 pink flowers.

I hope this helps.

Answer 3

If 1/8 are red and 1/4 are purple then 1/8 + 1/4 are red or purple

1/8 + 1/4 = 1/8 + 2/8 = 3/8

So since 3/8 are either red or purple, and there are 128 total flowers then 3/8•128 are either red or purple.

3/8•128 = 3/8•128/1 = (3•128)/(8•1) = 384/8 = 48 so 48 are either red or purple. That means 128 - 48 or 80 are NOT red or purple.

Of these 80, 1/4 are pink. 1/4 of 80 is 20 so 20 are pink