SOLUTION: 1) The value of a two-digit number exceeds twice the sum of its digits by 19. The tens digit is two less than the units digit. Find the number.
2) Farmer Hanson is putting toget
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Question 892573: 1) The value of a two-digit number exceeds twice the sum of its digits by 19. The tens digit is two less than the units digit. Find the number.
2) Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples in each basket and the same number of pears in each basket?
Please explain, I do not understand these questions. Thank you!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1) The value of a two-digit number exceeds twice the sum of its digits by 19.
The tens digit is two less than the units digit. Find the number.
let a = the 10's digit
let b = the units
then
10a+b = the number
Write an equation for each statement,simplify as much as possible
"The value of a two-digit number exceeds twice the sum of its digits by 19."
10a + b = 2(a+b) + 19
10a + b = 2a + 2b + 19
10a - 2a + b - 2b = 19
8a - b = 19
:
"The tens digit is two less than the units digit."
a = b - 2
a - b = -2
Use elimination on these two equations
8a - b = 19
a - b = -2
-------------Subtraction eliminates b, find a
7a = 21
a = 21/7
a = 3
we know that a = b - 2, therefore
3 = b - 2
3 + 2 = b
b = 5
25 is the number, you can check this for yourself in both statements
:
:
2) Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples in each basket and the same number of pears in each basket?
:
If you have to use up all the fruit, then 8*30 and 5*30 (highest common divisor)
8 apples, 5 pears, in 30 baskets
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