Answer:
a)
x | y
==========
16 | 3
12 | 6
8 | 9
4 | 12
b) A large basket contains 23 eggs
Step-by-step explanation:
a) Isolating 3x, we get
3x = 60-4y
This means that 60-4y is a multiple of 3.
Besides, as x is a positive integer, then x = 60-4y has to be greater than zero
60-4y>0
Solving the inequality for y
60>4y
60/4 > y
15>y (or y<15, which is the same)
The multiples of 3 which are smaller than 15 are 3,6,9 and 12
Now we draw a table for these values of y and found the value of x by replacing in the equation 3x = 60-4y---> x = (60-4y)/3
x | y
=======
16 | 3
12 | 6
8 | 9
4 | 12
And these are all the solutions in positive integers.
b) This problem is pretty much like problem a)
Let's call x the number of eggs contained in the large baskets and y the number of eggs contained in the small baskets.
Then
Number of eggs bought - number of eggs sold = number of eggs left over.
In this case
11x-39y = 19
But we also know that 0<y<12 because the small baskets hols fewer than a dozen.
Isolating x in the equation 11x-39y + 19, we get
x=(19+39y)/11
Now we make a table with these values of x and y remembering that y is a positive integer smaller than 12
x | y
=======
5.2 | 1
8.8 | 2
12.4 | 3
15.9 | 4
19.5 | 5
23 | 6
26.6 | 7
30.1 | 8
33.6 | 9
37.2 |10
40.7 |11
From this table we see that the only integer solution for x is 23, so a large basket contains 23 eggs.
