Exercise 11 Page 230

We are given two guest checks and we want to find how much we would pay for 2 specials and 2 glasses of milk. To do so, let's write a system of equations. The first check says that 4 specials and 2 glasses of milk cost $28.00. Let x be the cost of one special and let y be the cost of one glass of milk. We can use this information to write the first equation. 4x+ 2y = 28 The second check says that 3 specials and 4 glasses of milk cost $26.25. Let's write the second equation. 3x+ 4y = 26.25Let's combine these two equations into a system of equations. 4x+2y = 28 3x+4y = 26.25 Note that we can multiply the first equation by 2 so that the coefficients of y are the same in both equations. Then, we can subtract the second equation from the first one. Let's do it!

4x+2y = 28 & (I) 3x+4y = 26.25 & (II)

▼

(I):LHS * 2=RHS* 2

MultEqn

(I): LHS * 2=RHS* 2

2(4x+2y) = 2(28) 3x+4y = 26.25

Distr

(I):Distribute 2

2(4x)+2(2y) = 2(28) 3x+4y = 26.25

Multiply

(I):Multiply

8x+4y =56 3x+4y = 26.25

SysEqnSub

(I): Subtract (II)

8x+4y-( 3x+4y) =56- 26.25 3x+4y = 26.25

Distr

(I): Distribute -1

8x+4y-3x-4y =56-26.25 3x+4y = 26.25

SubTerms

(I): Subtract terms

5x =29.75 3x+4y = 26.25

DivEqn

(I): .LHS /5.=.RHS /5.

5x/5 =29.75/5 3x+4y = 26.25

CalcQuot

(I):Calculate quotient

x =5.95 3x+4y = 26.25

Now that we know the value of x, we can substitute it into the second equation to find y.

x =5.95 3x+4y = 26.25

Substitute

(II): x= 5.95

x =5.95 3(5.95)+4y = 26.25

Multiply

(II): Multiply

x =5.95 17.85+4y = 26.25

SubEqn

(II): LHS-17.85=RHS-17.85

x =5.95 17.85+4y-17.85 = 26.25-17.85

SubTerms

(II):Subtract terms

x =5.95 4y = 8.40

DivEqn

(II): .LHS /4.=.RHS /4.

x =5.95 4y/4 = 8.40/4

CalcQuot

(II):Calculate quotient

x =5.95 y = 2.10

We found that x =5.95 and y = 2.10. This means that one special costs $5.95 and one glass of milk costs $2.10. We want to find how much it costs for 2 specials and 2 glasses of milk. This means that we want to evaluate the following expression. 2x + 2y Let's substitute x =5.95 and y = 2.10.

2x + 2y

SubstituteII

x= 5.95, y= 2.10

2( 5.95) + 2( 2.10)

Multiply

Multiply

11.90 + 4.20

AddTerms

Add terms

16.10

We found that 2 specials and 2 glasses of milk cost $ 16.10.