SOLUTION: If 3 doughnuts and 2 cookies equal 2.98. And 1 doughnut and 3 cookies equal 2.23. How much does 1 doughnut and one cookie equal.
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Question 108953: If 3 doughnuts and 2 cookies equal 2.98. And 1 doughnut and 3 cookies equal 2.23. How much does 1 doughnut and one cookie equal.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let D represent the value of doughnuts and C represent the value of cookies.
.
The first sentence tells you that 3 doughnuts and 2 cookies have a value of 2.98. In equation
form you can write this as:
.
3D + 2C = 2.98
.
The second sentence tells you that 1 doughnut and 2 cookies have a value of 2.23. In equation
form you can write this relationship as:
.
1D + 3C = 2.23
.
Write these two equations one above the other to get:
.
3D + 2C = 2.98
1D + 3C = 2.23
.
Notice that if you multiply the bottom equation (all terms on both sides) by 3 the set
of equations becomes:
.
3D + 2C = 2.98
3D + 9C = 6.69
.
Next subtract the bottom equation from the top equation ... vertically and the terms 3D
and 3D disappear. You are left with the equation:
.
-7C = -3.71
.
Now you can find the value of C by dividing both sides by -7 to get:
.
C = -3.71/-7 = 0.53
.
Now that you know C = 0.53 you can solve for D by returning to either of the two equations
and substituting 0.53 for C. Let's return to the equation:
.
1D + 3C = 2.23
.
When you substitute 0.53 for C this equation becomes:
.
D + 3(0.53) = 2.23
.
Multiplying out the left side results in the equation becoming:
.
D + 1.59 = 2.23
.
Subtracting 1.59 from both sides to get rid of it on the left side reduces the equation to:
.
D = 0.64
.
So our answers are D = 0.64 and C = 0.53
.
You were asked to find the sum of 1 doughnut and 1 cookie. The answer is:
.
D + C = 0.64 + 0.53 = 1.17
.
Hope this helps you to understand the problem a little better.
.
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