Answer:
The change will be $4.75
Step-by-step explanation:
Given data:
<u>Monday </u>
Total paid = 5.45
milk bought =3
coffee bought = 4
doughnuhts = 7
<u>Tuesday</u>
Total paid = 5.30
milk bought =4
coffee bought = 2
doughnuhts = 8
<u>Wednesday</u>
Total paid = 5.15
milk bought =2
coffee bought = 5
doughnuhts = 6
<u>Thursday</u>
Total paid = X
milk bought =5
coffee bought = 2
doughnuhts = 9
<em>Let milk be m, Let coffee be c and Let doughnuts be d</em>
3m + 4c + 7d = 5.45 <em>(eqaution 1)</em>
4m + 2c + 8d = 5.30 <em>(equation 2)</em>
2m + 5c + 6d = 5.15 <em>(equation 3)</em>
<em>Using equation 1 and equation 2 ( to eliminate m)</em>
3m + 4c + 7d = 5.45 <em>(Multiply the whole equation by 4)</em>
4m + 2c + 8d = 5.30 <em>(Multiply the whole equation by 3)</em>
12m + 16c +28d = 21.8
12m + 6c +24d = 15.9 <em> (Subtracting the two equations)</em>
0m +10c + 4d = 5.9
therefore 10c +4d = 5.9 <em>(equation 4)</em>
<em>Using equation 2 and equation 3 (to eliminate m)</em>
4m + 2c + 8d = 5.30 <em>(Multiply the whole equation by 2)</em>
2m + 5c + 6d = 5.15<em> (Multiply the whole equation by 4)</em>
8m + 4c + 16d = 10.6
8m +20c +24d = 20.6 <em>(Subtracting the two equations)</em>
0m -16c -8d = -10
-16c -8d = -10 <em>(equation 5)</em>
<em>Solving equation 4 and equation 5( to eliminate d)</em>
10c +4d = 5.9 <em>(Multiply whole equation by 8)</em>
-16c -8d = -10 <em>(Multiply whole equation by 4)</em>
80c + 32d = 47.2
-64c -32d = -40 <em>(Adding the equations)</em>
16c =7.2
<em>therefore</em> c = 0.45
<em>Substituting into equation 4</em>
10(0.45) + 4d = 5.9
4.5 + 4d = 5.9
4d = 5.9-4.5
4d = 1.4
therefore d = 0.35
<em>Substituting c and d into equation 1</em>
3m + 4c + 7d = 5.45
3m + 4(0.45) + 7(0.35) = 5.45
3m + 1.8 + 2.45 = 5.45
3m = 5.45-2.45-1.8
3m = 1.2 therefore m = 0.4
Alphonse has to pay 3m + 2c + 9d
Alphonse change will be 10 - (3m + 2c + 9d) <em>(Substituting m, c and d)</em>
10- (3(0.4) + 2(0.45) + 9(0.35) = 10 -(1.2+0.9+3.15)
<em>which simplifies</em> to 10- 5.25=4.75
The change will be $4.75
