how do you do these math problems?(9th grade algebra)?
rachel has a stack of coins worth $4.00. She has twice as many dimes as nickels. She has 6 more quarters than nickels. How many of each coin does she have?
AND
Speed seed company mixes bluegrass seed that costs $7.60 per lb. with ryegrass seed that costs $6.25 per lb. how many lbs of bluegrass seed should be mixed with 200 lbs. of ryegrass seed to make a mixture worth $7.00 per lb.?
we're supposed to make a table then with that make an equation
Comments
These types of problems can be solved using systems of equations. To do that, find the variables that each problem is asking you to solve for, then use the information given in the problem to write expressions relating the variables to each other. You should be able to end up with as many expressions as there are variables.
The first problem asks for numbers of nickels, dimes, and quarters. Let n be the number of nickels, d be the number of dimes, and q be the number of quarters. Next, translate each piece of information given in the problem into a mathematical equation.
There are twice as many dimes as nickels: d = 2n
There are 6 more quarters than nickels: q = n + 6
The coins total $4 (400 cents) in worth: 5n + 10d + 25q = 400
Right away, you have expressions for both d and q in terms of n, so you can substitute those into the equation for total worth and solve for n. The value of n can then be used to solve for q and d.
The second problem is a bit tricky as it's not immediately obvious what the variables are. I don't know exactly what would be meant by using a table in this case (sorry!), but hopefully I can show how to derive the equations you should arrive at.
From the wording of the question, you know that one variable has to be the number of pounds of bluegrass. Let that be b. You can find another variable to relate it to if you consider how you would determine the price per pound of a mixture: divide the total price of the mixture by the total number of pounds it weighs. There's already a variable for pounds, so let the total price be another variable, p.
The problem tells you the desired price per pound of the mixture, so if you divide p by the total number of pounds of seed, you should get $7:
p / (200 + r) = 7
But how would you find the total price in the first place? You'd just multiply the price per pound of each seed, which you know, times the number of pounds of each:
p = 6.25 * 200 + 7.60 * r
This system of equations can be solved.
5(m+3)=2(a million+a million) <--- distribute each and every variables to the values equation interior 5m + 15 = 2 + 2 now upload 2+2 5m = 4 - 15 distribute 15 to precise hand section and subtract 5m = -11 now divide and ur finished wolah~ m = -11/5 or m = -2.2
5(m+3)=2(a million+a million) <--- distribute each and each variables to the values equation interior 5m + 15 = 2 + 2 now upload 2+2 5m = 4 - 15 distribute 15 to genuine hand component and subtract 5m = -11 now divide and ur carried out wolah~ m = -11/5 or m = -2.2