Need new strategy!!!

Question

A women promises to give her husband $20 for each day that he sticks to his diet, and the husband promises to pay her $5 for every day that he doesn't. After 30 days neither owes the other any money. How many days did the husband stick to his diet?

 

My first answer was 24, but I feel that this is incorrect. Please send me another strategy that I can use for questions like this. Thanks :)

Answer 1

x=# of days he sticks to his diet

30-x=# of days he doesn't stick to his diet

$20(x)=$5(30-x)

20x=150-5x

20x+5x=150

25x=150

x=150/25

x=6 days that he sticks to his diet

Answer 2

You had it backwards but were on the right track. This is a ratio problem

$20 for days stuck to diet compared to $5 for days he did not so put it in ratio or fraction form

 

20/5 and simplify the ratio by dividing both the top and bottom by 5 which gives me 4/1 now I multiply this by 30 days ( I know by looking at the ratio that 20 is four times larger than 5 so for every 1 day he stuck to the diet and earned $20 dollars, he did not stick to his diet for the next 4 days and paid $20 dollars)

 

To find my number of total days 4/1 x 30 = $120 which is the total amount paid by both the husband and the wife.

 

now 120 divided by $20 is 6 days he stuck to his diet

and 120 divided by  $5 is 24 day he DID not stick to his diet.

 

The easiest way to work these comparison problems is to set up a ratio between the two numbers in fraction form. Since the two numbers were both in dollars you set them up in the order given which puts the 20 on the top and the 5 on the bottom then simplify the fraction if possible.

 

I hope this helped you! You had the 24 number right but it was the number of days he DID not stick to his diet.

 

Have a great day

 

Linda C.