NEED HELP ASAP Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberries less than Ann and Ben together, what is the total number of strawberries the three of them ate?

Step-by-step explanation:

given:

Ann, Ben, and Cindy were eating strawberries.

The ratio of the numbers of berries they ate is 5:5:7.

If Cindy ate 30 strawberries less than Ann and Ben together,

find:

what is the total number of strawberries the three of them ate?

solution:

add the ratios 5 + 5 + 7 = 17

since Cindy ate 30, less than Ann and Ben together so, the equation is

7x = 5x + 5x - 30

7x - 10x = -30

x = 30/3

x = 10

ann 5 x 10 = 50

ben 5 x 10 = 50

cindy 7 x 10 = 70  

total            = 170

Explanation:

A = number Ann ate

B = number Ben ate

C = number Cindy ate

Let x be some positive whole number

Since A,B,C is in the ratio 5:5:7, this means

A = 5x

B = 5x

C = 7x

Note how A:B:C = 5x:5x:7x = 5:5:7. We divide all parts by x to simplify the ratio.

Cindy ate 30 strawberries less than Ann and Ben, so

C = A+B-30

C = 5x+5x-30

C = 10x-30

Earlier in the last section we had C = 7x, and now we found C = 10x-30

Since we're talking about the same C value, we can equate and solve

C = 7x

10x-30 = 7x ... replace C with 10x-30

10x-7x = 30

3x = 30

x = 30/3

x = 10

With this x value, we now know that...

A = 5x = 5*10 = 50

B = 5x = 5*10 = 50

C = 7x = 7*10 = 70

Cindy's count (70) is 30 less than Ann and Ben's combined count (50+50 = 100), so that helps confirm the answer.

Further confirmation comes from 50:50:70 reducing to 5:5:7 when you divide all parts by the GCF 10.

The last step is to add the values of A, B and C.

A+B+C = 50+50+70

A+B+C = 100+70

A+B+C = 170

Side note: since A+B+C = 5x+5x+7x = 17x, this means that the final answer is a multiple of 17.