Problem

The value of all the nylon brushes that a paint s…

03:06

Problem 9 Medium Difficulty

a. Two antifreeze solutions are combined to form a mixture. Complete the table and then form an equation for this mixture problem.
b. Two oil-and-vinegar salad dressings are combined to make a new mixture. Complete the table and then form an equation for this mixture problem.
(TABLE CAN'T COPY)

Answer

A. 0.05x=1.2
B. 3x=20

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Algebra

Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

this is a two part problem. So the first part part a reads to answer free solutions are combined to form a mixture, complete the table and then Forman equation for this mixture problem. So we have the chart using the equation amount time strength is equal to pure answer. Freeze. We have a road for week strong and then the mixture, and we know that the amount of the week is X and we know that the amount for the strong is six. And we know the strength for all three solutions. So the strength of the week solution is 25% which, as a decimal 0.25. The strength for the strong solution is 50%. So as a decimal lead, sir, 500.50 and the strength of the mixture is 30%. So as it s Malek 0.30. So the first thing that we're gonna do is fill in the amount of the mixture, and that's gonna be X plus six. Since it's a combination of the weak and the strong solution, and then so find out the amounts of pure antifreeze, we're gonna have to multiply the amount times a strength for all three solutions. So for the week it's gonna be 0.25 x for the strong. It's going to be 0.50 time six and that is three. And then for the mixture, it's going to be 0.30 times X plus six. Yeah, so now we have to write an equation for this situation. So I'm gonna combine the pure answer, freeze for the weak and the strong and make it equal to the mixture. So we have 0.25 x plus three is equal to 0.30 times X plus six. So from here, I'm gonna have to distribute the 0.32 the X as well asses to the six. So then we have 0.25 x plus three is equal to we have 0.30 times X, which is your 0.30 x, and then we have 0.30 ton six, which is 1.8. So now we want to get the light terms onto the same side. So I'm gonna first of track 0.25 x on both sides of the equation. 0.25 x minus 0.25 x zero. So then we have three is equal to We have 0.30 x, minus 0.25 x, and that 0.5 x plus 1.8 And now we can subtract 1.8 on both sides of the equation. So we have three minus 1.8, and that's 1.2 and then we have 0.5 x So we have 1.2 is equal to 0.5 x as our equation for this situation. Then for our second problem, we have to oil and vinegar salad dressings are combined to make a new mixture, complete the table and then foreman equation for this mixture problem. So we're using the same equation. Amount time. Strength is equal toe pure vinegar this time, and we have a row for weeks strong and mixture. In this case, we don't know the amount of week vinegar, but we do know that the mixture is 10 and that the strong is represented by X, so the amount of week would be 10 minus x. Then, to find the pure vinegar in each dressing, we're gonna have to multiply the amount times the strength. So for the week, it's gonna be 0.3 times 10 minus X. For the strong, it's gonna be 0.6 x. And for the mixture, it's gonna be 10 times 0.5 which is 0.50. And then from here, we're going to combine the pure vinegar in the weak and the strong and make it equal to the mixture. So we have 0.3 times 10 minus X plus 0.6 X is equal to 0.50. So we're actually gonna multiply both sides of the equation by 101st to get rid of the decimals, and then we're gonna have to distribute the 100. So the 0.3 as well as the 0.6 x so 100 times 0.3 is just three. And then we still have to multiply the three by the 10 minus X and then 100 times their points there. Six x is six X and then we have 0.50 times 100 which is 50 from here. We're gonna have to distribute the three to the 10 as well as to the negative X. So we have three times sandwiches 30 and then three times negative X, which is negative. Three X plus six X is equal to 50. From here, we're gonna combine like terms. So we have the negative three explosives, six x So we have 30 three negative three X plus six x is three x so positive three x we're gonna do plus three X is equal to 50. And then from here we wanna get the 30 to the other side. So we're going to subtract 30 on each side, 30 minus 30 0 So then we have three. X is equal to 20 and that is our equation for the second situation.

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