Answer:
An apple costs £0.25
A banana costs £0.34
Step-by-step explanation:
Let a be apples and b be bananas.
10a+5b=4.2
8a+10b=5.4
Solve for a:
10a+5b=4.2
<em>Subtract 5b from both sides</em>
10a=4.2-5b
<em>Subtract 4.2 from both sides</em>
10a-4.2= -5b
<em>Multiply both sides by -1</em>
-10a+4.2=5b
8a+10b=5.4
<em>Subtract 10b from both sides</em>
8a=5.4-10b
<em>Subtract 5.4 from both sides</em>
8a-5.4= -10b
<em>Multiply both sides by -1</em>
-8a+5.4= 10b
<em>Divide both sides by 2</em>
-4a+2.7=5b
<u>Combine equations:</u>
-4a+2.7= -10a+4.2
<em>Add 10a to both sides</em>
6a+2.7=4.2
<em>Subtract 2.7 from both sides</em>
6a=1.5
<em>Divide both sides by 6</em>
a=0.25
An apple costs £0.25
Solve for b:
10a+5b=4.2
<em>Subtract 10a from both sides</em>
5b= -10a+4.2
<em>Subtract 4.2 from both sides</em>
5b-4.2= -10a
<em>Multiply both sides by -1</em>
-5b+4.2=10a
8a+10b=5.4
<em>Subtract 8a from both sides</em>
10b= -8a+5.4
<em>Subtract 5.4 from both sides</em>
10b-5.4= -8a
<em>Divide both sides by 4</em>
2.5b-1.35= -2a
Multiply both sides by 5
12.5b-6.75= -10a
<em>Multiply both sides by -1</em>
-12.5b+6.75=10a
<u>Combine equations:</u>
-12.5b+6.75= -5b+4.2
<em>Add 12.5b to both sides</em>
6.75=7.5b+4.2
<em>Subtract 4.2 from both sides</em>
2.55=7.5b
7.5b=2.55
<em>Divide both sides by 7.5</em>
b=0.34
A banana costs £0.34
If you would like to check and see if it is true, (I already checked, it is) you can use the formulas I gave at the start of the explanation.
10a+5b=4.2
8a+10b=5.4
a=0.25
b=0.34
