Question

The Star television costs $750 more than the Jupiter television. The two models cost $2,600 all together. Sandra writes an

equation to find the cost of the two models. If c represents the cost of the Jupiter television, which of the following would be
true when verifying the solution of the equation? Check all that apply.
Sandra substitutes C=925 into the equation C+(C+750) = 2,600.
Sandra substitutes C=925 into the equation C+(C-750) = 2,600
Sandra finds a true statement after substituting 925 into the equation.
Sandra finds a false statement after substituting 925 into the equation.
When Sandra evaluates the equation with c = 925, she subtracts 750 from 925. Then, she adds that sum to 925. She finds
that the value is not equal to 2,600.
When Sandra evaluates the equation with c = 925, she adds 925 to 750. Then, she adds that sum to 925. She finds that
the value is 2.600.

Answer 1

A. Sandra substitutes c = 925 into the equation c + (c + 750) = 2,600.

C. Sandra finds a true statement after substituting 925 into the equation.

F. When Sandra evaluates the equation with c = 925, she adds 925 to 750. Then, she adds that sum to 925. She finds that the value is 2,600.

Answer 2

-Sandra finds a true statement after substituting 925 into the equation.

-When Sandra evaluates the equation with c = 925, she adds 925 to 750. Then, she adds that sum to 925. She finds thatthe value is 2.600.

-Sandra substitutes C=925 into the equation C+(C+750) = 2,600.

Explanation:

#First we equate and solve for C

Given that Star=C+750 and Jupiter=C and that their combined cost is $2600:

`C+C+750=2600\\\\2C=1850\\\\C=925`

-Having calculated the value of C, we evaluate the statements

#Sandra substitutes C=925 into the equation C+(C+750) = 2,600.

-This is a true statement as the calculated value of C above is $925

# Sandra substitutes C=925 into the equation C+(C-750) = 2,600

`C+(C-750)=2600\\2C=3350\\\\C=1675`

This is false as the value $1675 is not equal to the true value of C($925)

#Sandra finds a true statement after substituting 925 into the equation.

-This is true as it equals to the true value of C($925).

#Sandra finds a false statement after substituting 925 into the equation.

False. $925 perfectly balances the equation as calculated above.

#When Sandra evaluates the equation with c = 925, she subtracts 750 from 925. Then, she adds that sum to 925. She finds

that the value is not equal to 2,600.

False. The aim is to add the individual prices of the TV sets and therefore no subtraction is involved in their prices.

#When Sandra evaluates the equation with c = 925, she adds 925 to 750. Then, she adds that sum to 925. She finds that

the value is 2.600.

`C+(C+750)=2600\\\\925+925+750=2600`

Hence, TRUE.