Question

large pies cost $5, and small pies cost $2. if 45 pies were sold for $120, how many small pies were sold ?

Answer 1

35 small pies

Explanation:

Framing system of linear equations and solving:

Let the number of large pies be 'l' and

The number of small pies be 's'.

Total pies sold = 45

⇒ l + s = 45 ------------(I)

l = 45 - s -------(II)

Cost of 45 pies = $120

Cost of 1 large pie = $5

Cost of 'l' large pies = 5*l = 5l

Cost of 1 small pie = $2

Cost of 's' small pie = 2*s = 2s

5l + 2s = 120 --------------(III)

Solving : substitution method

Substitute l = 45 -s in equation (III)

5*(45 - s) + 2s = 120

5*45 - 5*s + 2s = 120

225 - 5s + 2s = 120 {Combine like terms}

225 - 3s = 120

-3s = 120 - 225 {Subtract 225 from both sides}

-3s = -105

s = -105 ÷ (-3) {Divide both sides by (-3)}

s = 35

Substitute s = 35 in equation (II),

l = 45 - s

= 45 - 35

l = 10

`\sf \boxed{\text{\bf 35 small pies were sold}}`