Question 1186176

Mrs Thomas baked 3 types of cookies for sale.
She baked 24 more walnut cookies than cashew nut cookies.
She baked 48 more cashew nut cookies than almond cookies

Mrs Thomas then sold 2/3 of the walnut cookies, 3/4 of the cashew nut cookies and
1/2 of the almond cookies. She had 140 cookies left at the end of the sale.
How many walnut cookies did Mrs Thomas bake?
<pre>Let number of walnut be W
Then number of cashew = W - 24
Number of almond: W - 24 - 48 = W - 72


After selling {{{2/3}}} of the walnut, she had {{{(1/3)W}}}, or {{{W/3}}} left
After selling ¾ of the cashew, she had ¼ * (W - 24) = {{{W/4 - 6}}} left
After selling ½ of the almond, she had ½ * (W  -  72), or ½W - 36 left

We then get: {{{matrix(2,3, W/3 + W/4 - 6 + (1/2)W  -  36, "=", 140, W/3 + W/4 + (1/2)W, "=", 182)}}}
                   4W + 3W + 6W = 12(182) -------- Multiplying by LCD, 12
                            13W = 12(182)
Number of walnut sold, or {{{highlight_green(matrix(1,7, W, "=", 12(182)/13, "=", 12(14), "=", 168))}}}</pre>