The cost of 4 baseball bats and 3 softball bats is $389. If the baseball bats cost $10 less than the twice the hat, write an equation to model the
situation so that we can find the cost of the hat and the baseball bat.

    the price of a softball bat is 143 dollars, and the price of a baseball bat is 296 dollars.

Step-by-step explanation:

This is a problem that needs a set of equations because you are solving for two variables. The price of a baseball bat, and the price of a softball bat. To find the two equations in this sentence you take the context clues that are given to you. The first clue is that the cost of 4 baseball bats and 3 softball bats equals 389. Let's make b stand for the cost of a baseball bat, and s stand for the cost of a softball bat. The equation we can get from this piece of information is 4b +3s = 389 dollars. The second piece of information we get is that the baseball bats cost ten dollars less than twice the softball bat price. This is another equation that is b-10 = 2s.

    Now that we have both of the hidden equations, we can solve them to find the cost of baseball bats, and softball bats.

    First step is to solve one of the equations to get either one of the variables by themselves. I chose the second one, because it takes less steps. b-10 = 2s. If you add ten to both sides you get the variable b by itself in the equation: b = 2s - 10. Now we go back to the first equation, and substitute in 2s - 10 wherever there is a b. This makes equation one look like this: 4(2s - 10) +3s = 389. Now it is a solvable equation.  First you distribute the 4 to (2s - 10) you get 8s - 40 +3s = 389. Then you can add 8s and 3s together since they are the same variable. 11s - 40 = 389. Next, add the 40 to both sides to cancel it out, and you get that 3s = 429. Finally, divide both sides by 3 to get what s equals. s = 143.

    Now that we have the value of s, we can go back to the first equation and plug that value in to solve for b. This makes the first equation: b - 10 = 2(143).

Multiply the 2 and 143 first. Then, your equation looks like: b - 10 = 286. Finally, add the 10 to both sides to cancel it out and you get that b = 296.

    Putting this back into context: the price of a softball bat is 143 dollars, and the price of a baseball bat is 296 dollars.