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One type of granola has nuts, by mass. A second type of granola has nuts. What mass of each type needs to be mixed to make of granola that will have nuts?
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Q. One type of granola has nuts, by mass. A second type of granola has nuts. What mass of each type needs to be mixed to make of granola that will have nuts?
- Define variables: Let be the mass of the first type of granola ( nuts) and be the mass of the second type of granola ( nuts). We know the total mass of the mixture should be . So, the equation is:
- Set up equations: Next, we set up the equation for the nut content. The total nut content in the final mixture should be of , which is . The nut content from the first type is and from the second type is . The equation is:
- Solve equations: We can solve these equations simultaneously. From the first equation, express in terms of :
- Substitute values: Substitute in the second equation:
- Final solution: Substitute back into the equation for :
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