Here you have two unknowns, so you would need two equations (system of equations). By using w to represent walnuts and c to represent chocolate chips your equations would be 5w + 2c = 10 and 3w + 8c = 23, the coefficients being the amount of pounds of walnuts and chocolate chips and the right hand side of the equations being the total price. From there you can either solve for one variable in terms of the other and plug in to the other equation, or you could subtract one equation from the other ( I personally prefer solving for one variable in terms of the other and then plugging in to the other equation).
False: although the size increases to its ratio, it is not considered similar
Answer:
12.75w + 25 = 114.25
w = 7
Step-by-step explanation:
since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet) we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.
to find out what w represents, we have to solve for it. solving for w means isolating it on one side. so, what we can do first is subtract 25 from both sides. that would then make the equation:
12.75w = 89.25
now, we have only one step left to isolating w, and that's to get 12.75 on the other side somehow. since we're multiplying 12.75 with w, and we're applying additive inverse properties, meaning the opposite of what is happening to cancel it out on the side it's in, we would divide 12.75 on both sides. in the left, 12.75 would cancel out, and in the right, we would divide 89.25 by 12.75. the quotient is 7.
now there's nothing left to take out to isolate w, so we have:
w = 7
sarah saved up for 7 weeks.
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