Solve the following system of equations
1 answer:
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Angelo bought 14 apples and 6 bananas
<em><u>Solution:</u></em>
Let "a" be the number of apples bought
Let "b" be the number of bananas bought
Cost of 1 apple = $ 0.50
Cost of 1 banana = $ 0.75
<em><u>He bought 20 pieces of fruit. Therefore,</u></em>
number of apples bought + number of bananas bought = 20
a + b = 20 -------- eqn 1
<em><u>He spent $ 11.50. Therefore, we frame a equation as:</u></em>
number of apples x Cost of 1 apple + number of bananas x Cost of 1 banana = 11.50
0.50a + 0.75b = 11.50 ------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
From eqn 1,
a = 20 - b ------ eqn 3
<em><u>Substitute eqn 3 in eqn 2</u></em>
0.50(20 - b) + 0.75b = 11.50
10 - 0.5b + 0.75b = 11.50
0.25b = 11.50 - 10
0.25b = 1.5
Divide both sides of equation by 0.25
<h3>b = 6</h3><em><u>Substitute b = 6 in eqn 3</u></em>
a = 20 - 6
<h3>a = 14</h3>Thus he bought 14 apples and 6 bananas