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Solve for the unknown amount. The formula $C=28 h+40$ describes the total cost for a plumber to visit a home, where $C$ is the total cost and $h$ is the number of hours on site. How long can the plumber work for Li if Li has 152 dollars?

In order to solve this equation, we first have to get the variables on the same side. So to do that we're going to pick the variable term with the smallest coefficient. And we're going to move that term to the other side using opposite operations. So out of our two variable terms eight C. And negative three. See the smallest one is negative three C. So that's the one. We're going to move to the other side since it's a negative three C. We're going to add a positive three C to both sides and make sure that you line your your terms up under the like terms, we can only add variables to other variables. So I'm putting the three C in line with the A. C. Mhm. So when we combine those eight C plus three, see that gives us 11 C plus seven. And then on the other side we have negative 37. So the next step to solve for the variable is going to be to subtract seven. The seven is currently being added to the variable, So the opposite of that would be to subtract seven from both sides. And that leaves us with 11 C. And then on the other side negative 37 minus seven is negative 44. And then finally ah we need to get rid of this 11. The sea is being multiplied by the 11th. So to get rid of it, we're gonna divide by 11 on both sides. When we divide by 11 we get C equals negative four. Mhm. So now we need to check our answer in order to check the answer. We're going to go back to the original equation from the beginning of the problem and we're going to be replacing all of the sea terms both of the season. The equation are going to be replaced with the negative four that we just found for an answer. So when we plug that in we have eight times negative four plus seven equals negative three times negative four minus 37. Now we just need to simplify this so we can perform these operations will start with the multiplication. So eight times negative four is negative 32 plus seven and negative three times negative four is positive 12 minus 37. Now we just need to combine the terms on each side. So on the left negative 32 plus seven is negative 25. Mhm. And on the right 12 minus 37 is also negative 25. So since we got the same number on both sides of the equation, that means our answer checks out. So our original answer C equals negative four is the correct solution for this equation.

So for problem 38 says saw this system of equations. You chose an exercise 37 it's also multiple choice. So we came up with to t plus two years equal toe $4.80 as well as three T plus easy goods of $4 for the previous problems. So now we're gonna have to solve for what the price of each taco was as well as the price of each enchilada. So I'm going to start with the second equation. I'm going to isolate the e, so I'm gonna get the e alone. So to do that, I'm gonna have to subtract three t on each side. So three T minus three t is zero. So that I'm left with e is equal to four minus three t and from here, I'm going to substitute or plug that in two the first equation. So now we have to t plus to Times E and in this case is for minus the three t is equal to 4 80 or $4.80. Then we have to t I'm gonna have to distribute the to to the four as well as a toots of the negative three t So we have to sums for is eight so positive eight and we have two times negative. Three t is negative. 60 is equal to $4.80. And then from here, I'm gonna have to combine the light term. So I have to t minus 60 and that is negative. 40 plus A is equal to $4.80. And from here, I'm going to subtract the eight. Since I want to get the constant to the other side. So eight minus 80 So then I have negative 40 is equal to 4.8 e minus eight is going to be negative. 3.20. And then from here, I'm gonna divide both sides by negative for so that I can isolate the price of the taco. So negative four divided by negative four is one. So I have t is equal to and the negative 3.28 divided by negative four and negative Spider by negative is positive. Three points when he had divided by four is 0.80 or 80 cents. So that means that each taco was 80 cents and then to figure out the price of an enchilada. I'm gonna have to plug in 80 cents 40. And our equation that we came up with for enchiladas so we have is equal to four minus three times t. So instead of writing team in a right 0.80 now I have is equal to four minus. I have three times 0.80 and that's gonna be 2.40 or $2.40. And then, lastly, once I subtract four minus $2.40 I get $1.60. So that means that each enchilada is a dollar in 60 cents. Now have to look at the different answer choices to see which one has the prices that are correct. So Inter choice of has tacos are a dollar and 60 cents, So that's not correct. Answer. Choice G has Tacos are 80 cents, which is correct, and enchiladas or dollar 60 which is also correct. So the correct answers choice is G. And then just to look and eliminate the other answer choices and the choice h has tacos are dollar 40 Each Answer choice Jay has tacos are 60 cents each. So the correct answer is in fact, G

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We're giving an equation in the variable. We were asked to solve this equation for this. Very. The equation is F equals 9/5 C plus 32 and were asked to solve for the variable. See, we went through this in the same way as an example one book. So first, multiply both sides by the least common denominator of both sides. So the least common denominator is going to be Please come nominator of 15 and one, which is five. So multiply both sides by five. Next step we want to dio is used the distributive property. And so, using the distributive property we get Flight F is equal to nine C plus 32 times five, 150 plus 10 which is 160. Next, we want to combine like terms on each side of the equation, which we've already done. Then we used the addition property of equality. So by the addition property of equality we have, that's nine C is equal to five minus 160 simply at negative 160 of those sides, and finally, or use the multiplication property of equality, isolate the variable so multiplying both sides by 1/9. We get C equals one knife times five, death minus 1 60 And in this last step, we'll use the distributive property again to get that C is equal to 5/9 if minus 1 60 divided by nine. We have that 1 60 is not divisible by three. So this is the lowest terms we can write it in. So this is another way to write C, so I would say that either of these would be acceptable answers.