1) Monica hands out 4 bars of chocolate to each of her brothers and finds that she has 5 left over. If she had

Question

given each brother 6 bars of chocolate instead, she would have been short of 3. How many brothers does Monica have ?

2) There are 2 types of star-shaped buttons in Mother's sewing kit : the 5-pointed stars & the 7-pointed stars. Mother sewed 15 star-shaped buttons onto Reiko's T-shirt. Out of those 15 stars, Reiko counted 91 points. How many of each kind of star were sewn onto Reik's T-shirt ?

Answer 1

b=number of brothers
4b+5=6b-3 since the number of chocholate bars are the same
2b=8
b=4 brothers

2) 5 pt stars=a, 7 pt stars=b
5a+7b=91
a+b=15 (times 5 to eliminate one variable)
5a+5b=75 subtract from the first

2b=16 b=8 a=7
checking the math
5(7)+7(8)=91
35+56=91 yes

Answer 2

I'll do 1) for you, and see if you can figure out 2)

Suppose Monica has x brothers. Then, according to the information given, she must have 4*x + 5 candy bars.

According to the second scenario, Monica should have 6*x - 3 candy bars.

Of course she must have the same number of candy bars in each case, so 4*x + 5 = 6*x - 3.

When you solve for x, you get x = 4. Monica has 4 brothers.

Answer 3

1) Four Brothers! 4x4+5=21 (4x6=24) She had 21 bars therefore she would come up short 3 if she were to try and give each 6 bars.

2) seven 5-starred and eight 7-starred. (7x5+8x7=35+56=91)

Answer 4

2) 8 lots of 7 pointed stars
7 lots of 5 pointed stars

Answer 5

she has too much chocolate!