Emily M. answered • 01/26/15

Tutor

5
(2)
BS in Chemistry for Math, Science, and Test Prep

First, start off by building your equations. Assign names to your

**variables**:**carrot**= number of calories per carrot

**chocolate**= number of calories per carrot

B ate 10 carrots and 7 chocolates, total cals were 263:

Equation B: 10*

**carrot**+ 7***chocolate**= 263F ate 4 carrots and 8 chocolates, total cals were 230:

Equation F: 4*

**carrot**+ 8***chocolate**= 230Pick one of the equations (either that for B or F), solve for one of the variables (either carrot or chocolate), then insert this solution into the

*other*equation.For example, I'm going to start with Equation F and solve for carrot:

4*carrot + 8*chocolate = 230

(-8*chocolate) (-8*chocolate) (subtracting 8*chocolate from both sides)

4*carrot = 230 - 8*chocolate

(÷4) (÷4) (dividing both sides by 4)

carrot = (230 - 8*chocolate)÷4

**(Distributive Property)****carrot = 57.5 - 2*chocolate**

Plug this solution into Equation B:

10*

**+ 7*chocolate = 263 (insert solution for "carrot" into Equation B)***carrot*10*

**(57.5 - 2*chocolate)**+ 7*chocolate = 263Now, solve for "chocolate":

First simplify:

10*(57.5 - 2*chocolate) + 7*chocolate = 263 (Distributive property)

575 - 20*chocolate + 7*chocolate = 263 (Simplify)

575 - 13*chocolate = 263

(-575) (-575) (Subtract 575 from both sides)

-13*chocolate = -312

(÷-13) (÷-13) (Divide both sides by -13)

**chocolate = 24 calories**

Plug this into either equation B or F and solve for "carrot":

Equation F: 4*carrot + 8*

**chocolate**= 230 (Plug in chocolate = 24)4*carrot + 8*

**24**= 230 (Simplify: 8*24 = 192)4*carrot + 192 = 230

(-192) (-192) (Subtract 192 from both sides)

4*carrot = 38

(÷4) (÷4) (Divide both sides by 4)

**carrot = 9.5 calories**

Check your work, plug answers into both equations and see if they add up:

Equation B: 10*carrots + 7*chocolates = 263

10*9.5 + 7*24 = 263

Equation F: 4*carrot + 8*chocolate = 230

10*9.5 + 7*24 = 263

Equation F: 4*carrot + 8*chocolate = 230

4*9.5 + 8*24 = 230

**The answers chocolate = 24 calories and carrot = 9.5 calories are correct.**