For large parties of children, a restaurant uses a formula to determine the number of ice cream bars to buy if c children will attend. Ice cream bars are sold only in boxes of 24. If 14 boxes of bars were bought when children 150 attended, and if 16 boxes were bought when 175 attended, which of the following could be the formula used by the restaurant?

a) b= c+25
b) b= c+175
c) b=2c
d)b=2c+25
e)b=3c+10

According to collegeboard, choice d is correct. They say that is c=150, then b=2(150)+25=325, and 325=13(24)+13, can someone please explain to me where they got the 13 from and why d

Question

For large parties of children, a restaurant uses a formula to determine the number of ice cream bars to buy if  c children will attend. Ice cream bars are sold only in boxes of 24. If 14 boxes of bars were bought when children 150 attended, and if 16 boxes were bought when 175 attended, which of the following could be the formula used by the restaurant?
 
a) b= c+25
b) b= c+175
c) b=2c
d)b=2c+25
e)b=3c+10

According to collegeboard, choice d is correct. They say that is c=150, then b=2(150)+25=325, and 325=13(24)+13, can someone please explain to me where they got the 13 from and why d