The nut house offers a mixture of soy nuts and almonds, almonds, self for seven dollars per pound is toilets sale for $5.50 per pound. The nuthouse will make 20 pounds of mixed nuts in silver mixture for $5.95 per pound. The following equations represent the problem of keeping the cause of the mixture, consistent with the ingredients. How many pounds of signage should be used in the mixture solve for Y
Let's assume that the weight of the soy nuts is represented by variable X.
According to the problem, the cost of soy nuts is $7 per pound.
Therefore, the cost of the soy nuts used in the mixture is 7X dollars.
Also, let's assume the weight of the almonds is represented by the variable Y.
According to the problem, the cost of almonds is $5.50 per pound.
Therefore, the cost of the almonds used in the mixture is 5.50Y dollars.
The nut house will make 20 pounds of mixed nuts, so the total weight of the mixture is 20 pounds.
According to the problem, the cost of the mixture is $5.95 per pound.
Therefore, the total cost of the mixture is 5.95 * 20 = 119 dollars.
Since the cost of the mixture consists of the costs of soy nuts and almonds, we can write the following equation:
7X + 5.50Y = 119
We need to solve this equation in order to find the value of Y.
To solve for the amount of soy nuts that should be used in the mixture, we can create the following equation:
Soy nuts cost: $7 per pound
Almonds cost: $5.50 per pound
Mixed nuts cost: $5.95 per pound
Let's assume the number of pounds of soy nuts used in the mixture is Y pounds.
The cost of the soy nuts would then be: $7 * Y = 7Y
The cost of the almonds used in the mixture would be: $5.50 * (20 - Y) = 110 - 5.50Y
The cost of the mixed nuts would be: $5.95 * 20 = 119
Since the cost of the soy nuts plus the cost of the almonds should equal the cost of the mixed nuts, we can set up the equation:
7Y + 110 - 5.50Y = 119
Now let's solve for Y.
7Y - 5.50Y = 119 - 110
1.5Y = 9
Y = 9 / 1.5
Y = 6
Therefore, 6 pounds of soy nuts should be used in the mixture.
To solve for the number of pounds of soy nuts (Y) that should be used in the mixture, we need to analyze the given information and set up an equation.
Let's break down the given information:
- The nut house sells soy nuts and almonds separately.
- Soy nuts cost $7 per pound.
- Almonds are on sale for $5.50 per pound.
- The nut house will make a mixture of soy nuts and almonds.
- They will make 20 pounds of mixed nuts.
- The cost of the mixture is $5.95 per pound.
To set up the equation, we can start by multiplying the number of pounds of soy nuts (Y) by the cost of soy nuts per pound ($7). Similarly, we multiply the number of pounds of almonds (20 - Y, since the total weight is 20 pounds and Y represents soy nuts) by the sale price of almonds per pound ($5.50). These two costs should add up to the total cost of the mixture per pound ($5.95):
Y * 7 + (20 - Y) * 5.50 = 5.95 * 20
Now, we can solve the equation:
7Y + (20 - Y) * 5.50 = 5.95 * 20
7Y + (110 - 5.50Y) = 119
Combining like terms:
7Y + 110 - 5.50Y = 119
1.50Y = 9
Y = 6
Therefore, we find that 6 pounds of soy nuts should be used in the mixture.