Need help solving Singapore 5 Challenging Word Problem!

[TrixieB]

I can't figure out how to set up this problem, from Challenging Word Problems 5, #15 on p. 8:

 

Janet bought a box of cookies for her friends. If she gives each of them 4 cookies, she will have 4 cookies left. If she gives each of them 5 cookies, she will need 5 more cookies. How many cookies are there in the box?

 

My dd wants to solve it by saying, "If there are 3 friends with 4 cookies, then there would be 16 cookies in the box. But if each friend had 5 cookies, then there would be 15 cookies in the box." Then she increases by one friend... I know this is not the way.

 

I am thinking some amount of groups of 4 plus 4 equals some amount of groups of 5 minus 5. But I can't figure out how to show this with a bar diagram...?

[AnnetteB]

DS says that it is 40...then I had to ask him how he just knew that off the top of his head! He says that the difference between +4 and -5 means she has 9 friends. I could see that the formula was y - 4x = 4 and y - 5X = -5 and that putting in the 9 friends at the x's would work out to the 40 cookies, but I am still amazed that he could "spit" the answer out with a glance over my shoulder. Some of us are obviously more math-minded.

[NicksMama-Zack's Mama Too]

DS says that it is 40...then I had to ask him how he just knew that off the top of his head! He says that the difference between +4 and -5 means she has 9 friends. I could see that the formula was y - 4x = 4 and y - 5X = -5 and that putting in the 9 friends at the x's would work out to the 40 cookies, but I am still amazed that he could "spit" the answer out with a glance over my shoulder. Some of us are obviously more math-minded.

 

IMHO!!

 

[_________?unknown____________][XXXX]

 

Illustrates the unknown amount she gave out and the extra 4.

 

 

[_________?unknown____________][XXXX]{XXXXX}

 

Illustrates the uknown amount, plus the extra 4 and additional 5 cookies that she had to come give out in the second scenerio.

 

 

Since she has to give one extra if she gives them 5, there must be 9 girls.

 

Hope this helps.

 

Now off to take an aspirin for my hurtin' head.

 

K

[TrixieB]

IMHO!!

 

[_________?unknown____________][XXXX]

 

Illustrates the unknown amount she gave out and the extra 4.

 

 

[_________?unknown____________][XXXX]{XXXXX}

 

Illustrates the uknown amount' date=' plus the extra 4 and additional 5 cookies that she had to come give out in the second scenerio.

 

 

Since she has to give one extra if she gives them 5, there must be 9 girls.

 

Hope this helps.

 

Now off to take an aspirin for my hurtin' head.

 

K[/quote']

My dd just now came up with the same answer.

 

Thanks to both of you! At least the problem is labeled "challenging" instead of "very easy practice problem for the mom whose brain stopped working some time ago" so I don't feel so bad! Who knew 5th grade math would strain my brain so much.