mixing $1.50/cup w/ $0.25/cup for 10 cups of $0.50/cup blend

[igor_iv837]

I"m struggling with this one too....

Ten cups of a restaraunts house Italian dressing is made by blending olive oil costing $1.50 per cup with vinegar that costs $.25 per cup. How many cups of each are used if the cost of the blend is $.50 per cup?

I wrote equatioan as x*1.50/ x* .25/ then 10 cups +2x*50...so its like this 1.75x=10+2x * .50 ......the answers dont come out right................

 

[Loren]

Re: One more please...

The number of cups times the cost per cup equals the total cost.

Name things. Total number of cups is to be 10. So, if you name number of cups of vinegar x, then number of cups of other stuff is 10 - x.
Build an expression that represents the total cost of x cups of vinegar. Build an expression that represents the total cost of 10-x cups of the other stuff. Build an expression that represents the total cost of the 10 cups of the mixture. Then build your equation on the basis that the total cost of cups of vinegar plus total cost of cups of other stuff equals the total cost of the mixture.

 

[arthur ohlsten]

Re: One more please...

let O be the number of cups of olive oil
let V be the number of cups of vinegar

eq.1) O+V=10 ten cups total
eq.2) total cost 10(.50)=$5
eq.3) O(1.5) + .25(V) =5

replace O in eq.3 with 10-V from eq.1

[10-V][1.5] +.25V=5 clear brackets
15 -1.5V +.25V =5 combine likes
15 -1.25V =5 add 1.25V to each side of = sign
15=1.25V +5 subtract 5 from each side
10 = 1.25 V divide each side by 1.25
8=V answer 8 cups of vinegar and 2 cups of oil

please check the answer
Arthur