SOLUTION: Baker Jack baked 160 cakes. 55% of them were walnut cakes and the rest were almond cakes. After selling some of the walnut cakes, the percentage of the walnut cakes become 40%. How

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Question 1199020: Baker Jack baked 160 cakes. 55% of them were walnut cakes and the rest were almond cakes. After selling some of the walnut cakes, the percentage of the walnut cakes become 40%. How many cakes were left ?
Found 2 solutions by math_tutor2020, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = number of walnut cakes sold

Jack baked 160 cakes.
55% of them are walnut
0.55*160 = 88 cakes are walnut

After selling x of walnut, he has 88-x walnut left.
This amount is divided over the amount of remaining cakes, 160-x.
This ratio is set equal to 0.40 to represent 40% of the remaining cakes are walnut.

(amount of walnut left)/(amount of cakes left) = ratio
(88-x)/(160-x) = 0.40

Let's solve for x
(88-x)/(160-x) = 0.40
88-x = 0.40(160-x)
88-x = 64-0.40x
-x+0.40x = 64-88
-0.60x = -24
x = -24/(-0.60)
x = 40

Jack sold 40 walnut cakes.
He started off with 88 of them, and now has 88-40 = 48 leftover.

160 total drops to 160-40 = 120 cakes left over.
48/120 = 0.40 = 40% of the remaining cakes are walnut.
We have confirmed the correct amount of walnut cakes sold.

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Answer: 120 cakes remain
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!

Baker Jack baked 160 cakes. 55% of them were walnut cakes and the rest were almond cakes. After selling some of the walnut cakes, the percentage of the walnut cakes become 40%. How many cakes were left ?
With 55% of the 160 being walnut, .55(160) = 88 were walnut

Let the number of walnut sold be W

Then after selling W walnut cakes, he’s left with 88 - W walnut cakes

Since 40% of the remaining cakes were walnut - after W walnut cakes were sold - then we have: 

                       .4(160 - W) = 88 - W ------- Cross-multiplying

                          64 - .4W = 88 - W

                         - .4W + W = 88 - 64

                               .6W = 24

Number of walnut cakes sold, or 

Thus, 160 - 40 = 120 cakes, were left 

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